PRT On-Time Performance Analysis

Summary

PRT on-time performance has declined over the 2019–2025 window and has not recovered to pre-COVID levels. A bus-only stratification confirms the decline is not an artifact of mixing modes – bus trends closely track the all-mode average.

Key Numbers

• 2019 baseline: ~69% all-mode weighted OTP, ~68% bus-only weighted OTP (93 routes reporting)
• COVID spike: 77% all-mode in March 2020 (low ridership improved adherence)
• Post-COVID trough: 60% all-mode weighted in September 2022
• Current level: 63–65% all-mode / 64–66% bus-only weighted OTP (late 2025)

Observations

• The unweighted and weighted averages now track very closely (~0.1 pp gap on average). The previous ~2-3 pp gap was an artifact of using SUM(trips_7d) across stops, which conflated trip frequency with route length and over-weighted long routes.
• The bus-only trend closely tracks the all-mode trend (gap averages ~0.5 pp), because bus routes (90+ of ~93 reporting) overwhelmingly dominate the system average. Rail's higher OTP lifts the all-mode average only slightly.
• Year-over-year change was consistently negative from mid-2021 through late 2022, then stabilized near zero – the system stopped declining but hasn't improved.
• Route count ranges from 68 to 96 across months. Most months have 93–96 routes, but Nov 2020 is a low outlier at 68 and mid-2025 months drop to 77–79. This varying composition does not affect the per-month averaging directly (each month averages whichever routes reported), but it means the set of routes being averaged is not fixed across time.
• For Jan 2019 – Mar 2021 (27 months), weights come from WPRDC time-varying scheduled trip counts. For Apr 2021 onward (56 months), weights fall back to static MAX(trips_7d)/7 from route_stops.

Caveats

• Time-varying weights are only available through Mar 2021. The static fallback for later months (MAX trips_7d / 7) is a single snapshot, not historical. If route frequency changed significantly after Mar 2021, the weighting for those months may not perfectly reflect actual service levels.
• The OTP definition ("on-time") is not specified in the source data – the threshold could be 1 minute, 5 minutes, or something else.
• Five routes (37, 42, P2, RLSH, SWL) have zero weight because they appear in neither scheduled_trips_monthly nor route_stops. These routes still contribute to the unweighted average.

Discussion

The central finding – that PRT OTP declined from ~69% to ~60% and has stabilized around 63–65% without recovering – is robust to the weighting methodology change. The overall trend shape (pre-COVID baseline, COVID spike, sustained decline, plateau) is visible in both weighted and unweighted series.

The collapse of the weighted-unweighted gap from ~2-3 pp to ~0.1 pp is itself a notable finding. The previous gap was interpreted as evidence that "high-frequency routes perform worse than low-frequency ones." This was wrong: it was an artifact of the SUM-across-stops weight, which inflated the weights of routes with many stops (i.e., long routes), not high-frequency routes. Once weights correctly reflect trip frequency (via WPRDC scheduled counts or MAX-based proxy), the weighted and unweighted averages converge, meaning route frequency does not systematically predict OTP at the system level. This is consistent with the null result from Analysis 10 (cross-sectional) and Analysis 30 (longitudinal panel).

The time-varying weights for the first 27 months (Jan 2019 – Mar 2021) capture real service changes, including the COVID-era cuts that reduced weekday trips by 31% between March and April 2020. This means the weighted OTP for 2020–2021 reflects actual service levels rather than retroactively applying today's schedule. The static fallback for later months remains a limitation – if PRT restructured service significantly after March 2021, those changes are not captured. Extending the WPRDC data or obtaining historical GTFS archives would close this gap.

The bus-only stratification confirms that system trends are driven by bus performance. Rail's higher OTP (~84%) lifts the all-mode average by only ~0.5 pp because bus routes represent >96% of the reporting routes. Any policy intervention to improve system OTP must focus on bus operations.

Methodology Change (2026-02-15)

Replaced static SUM(trips_7d) weighting with time-varying daily_trips from WPRDC scheduled trip counts (Jan 2019 – Mar 2021) and MAX(trips_7d)/7 static fallback for later months. This fixes Methodology Issues #1 (SUM conflation with route length) and #2 (static weights across 7 years). The weighted-unweighted gap collapsed from ~2-3 pp to ~0.1 pp, confirming the old gap was an artifact of the SUM-based weight inflation, not a genuine high-frequency penalty.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md – 5 issues (1 significant). Added bus-only trend line, fixed METHODS.md data section, documented route count variability (68–96), corrected "stable at 93" claim, and documented excluded routes.
• 2026-02-15: Fixed Methodology Issues #1 and #2. Switched to time-varying WPRDC trip weights for overlap period, MAX-based static fallback for remaining months.

Summary

Light rail consistently outperforms bus by a wide margin, and the difference is statistically significant (Mann-Whitney U = 6,563, p < 0.001). Among bus routes, dedicated right-of-way (busway) routes perform nearly as well as rail, and limited-stop variants beat their local counterparts.

Key Numbers

Statistical Tests

• Mann-Whitney U test (RAIL vs BUS monthly OTP): U = 6,563, p < 0.001 (n = 83 months each). Rail median monthly OTP = 86.1%, bus median = 69.2%. The difference is highly significant.
• Paired route comparison (2 pairs: 51/51L, 53/53L): Limited variants average +3.5 percentage points over their local counterparts (paired t-test: t = 7.37, p < 0.001, 95% CI: [+2.5, +4.4 pp], n = 85 paired monthly observations across 2 pairs). While the test is significant, the sample of only 2 route pairs limits the generalizability of this finding.
• Trip-weighted mode average: Bus trip-weighted OTP (66.8%) is about 2 pp below the unweighted average (68.9%), confirming that high-frequency bus routes tend to perform worse. Rail is nearly the same weighted (83.8%) vs unweighted (84.1%).

Observations

• Busway routes (P1, P3, G2) perform nearly as well as rail, consistent with the dedicated-right-of-way hypothesis.
• The previous classification grouped all P/G-prefix routes as "busway," which incorrectly included flyer routes like P17 (Lincoln Park Flyer), P78 (Oakmont Flyer), G3 (Moon Flyer), and G31 (Bridgeville Flyer). The corrected classification identifies only P1, P2, P3, and G2 as true busway routes.
• Only 2 local/limited pairs were found in the data (routes with matching base IDs). More pairs would strengthen the comparison.
• The RAIL–BUS gap has been roughly stable over time – both modes declined in parallel, suggesting system-wide factors rather than mode-specific ones.
• The INCLINE mode has no OTP data and was excluded.

Caveats

• Five UNKNOWN-mode routes (37, 42, P2, RLSH, SWL) were excluded from the analysis. P2 (East Busway Short) is plausibly a BUS/busway route, but its mode is listed as UNKNOWN in the database and it also lacks route_stops data.
• Bus route classification uses route ID naming conventions. True busway routes are identified as P1, P2, P3, G2; all other P/G/O-prefix routes are classified as flyers. Some routes may still be misclassified if their ID doesn't follow the standard pattern.
• Rail has only 3 routes (RED, BLUE, SLVR), so its average is sensitive to any single route's performance. The Mann-Whitney test has adequate statistical power due to 83 months of observations, but the underlying data comes from only 3 routes.
• The mode-level unweighted average treats each route equally regardless of trip volume. The trip-weighted version provides a ridership-adjusted perspective.
• Route composition varies across months (68–96 routes reporting). No balanced-panel filter is applied, so the set of routes contributing to each month's average is not fixed.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md – 6 issues (1 significant). Replaced "significantly outperforms" with formal Mann-Whitney U test, added paired t-test with 95% CI, excluded UNKNOWN-mode routes, fixed classify_bus_route to correctly distinguish busway from flyer routes, added trip-weighted mode comparison, and documented composition variability.

Summary

94 routes had sufficient data (12+ months) to rank. Rankings use trailing 12-month average OTP to reflect current performance, and post-2022 slope to capture recent trajectory without COVID distortion. Slopes now include 95% confidence intervals via scipy.stats.linregress; 51 of 94 slopes are statistically significant (CI excludes zero). 3 routes were flagged as high-volatility. Routes are ranked both overall and within their mode (BUS, RAIL, UNKNOWN).

Regression to the Mean

Caution: Extreme-ranked routes – both top/bottom performers and most-improving/declining – are expected to regress toward the mean in subsequent periods. This is a statistical phenomenon, not an operational one: routes that happen to have unusually good or bad stretches will tend to look less extreme next time, even without any intervention. Rankings should be interpreted as snapshots, not predictions. A route appearing at the top or bottom of a list does not necessarily mean it will stay there. Formal empirical Bayes shrinkage could partially correct for this, but is beyond the scope of this analysis. Readers should weight these rankings accordingly, especially for routes with fewer observations or higher volatility.

Top 5 Routes (by trailing 12-month OTP)

All top 5 are BUS routes. The 3 RAIL routes rank 9th (SLVR, 78.8%), 12th (BLUE, 77.4%), and 30th (RED, 72.8%) overall.

Bottom 5 Routes (by trailing 12-month OTP)

Post-COVID Trends (2022 onward)

Slopes are computed via OLS with standard errors. Only statistically significant slopes (95% CI excludes zero) are listed below. 43 of 94 routes have slopes that are not statistically significant – their trend cannot be distinguished from flat.

Most improving (statistically significant):

Most declining (statistically significant):

Notable non-significant slopes: SWL (Outbound to SHJ) has a point estimate of -10.4 pp/yr but its 95% CI is [-34.7, +13.8] due to having only 13 observations over a 21-month span – the apparent steep decline cannot be statistically distinguished from zero.

Observation Span

Most routes with slopes have the full 47-month post-2022 span. Two routes have notably narrow observation windows:

• SWL (Outbound to SHJ): 13 observations over 21 months
• P2 (East Busway Short): 21 observations over 21 months (significant slope, but over less than half the full window)

Routes with narrow spans may have slopes that are less representative of sustained trends.

Observations

• Using trailing 12-month OTP shifts the rankings compared to all-time averages: G2 (West Busway) has improved markedly and now leads, while 71B (Highland Park) and 65 (Squirrel Hill) have deteriorated significantly.
• The post-COVID slope isolates recent trajectory without the structural break caused by the 2020 COVID ridership drop, which dominated full-period slopes.
• High-volatility routes (std > 2x median) include SWL, 15 (Charles), and 65 (Squirrel Hill), which have extreme month-to-month swings.
• 4 routes were excluded from ranking for having fewer than 12 months of data.
• 89 of the 94 ranked routes are BUS, 3 are RAIL, and 2 are UNKNOWN mode. Within-mode ranks are provided in the CSV to allow fair comparisons.

Missing Stop Count Data

5 routes lack stop count data because they have no entries in the route_stops table: SWL (Outbound to SHJ), 37 (Castle Shannon), 42 (Potomac), P2 (East Busway Short), and RLSH (Red Line Shuttle). Stop counts for these routes are reported as null.

Caveats

• Stop counts come from current data; historical stop counts may have differed.
• Post-COVID slope assumes a roughly linear trajectory from 2022 onward, which may not hold for all routes.
• Regression to the mean (see dedicated section above) means that top/bottom rankings and most-improving/declining lists overstate the persistence of extreme performance. These lists identify current outliers, not necessarily future ones.
• Routes with narrow observation spans (SWL, P2) have less reliable slope estimates even when statistically significant.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md — 7 issues (1 significant). Added RTM caveat, slope standard errors and 95% CIs, observation span tracking, within-mode rankings, zero-variance guard, updated METHODS.md for post-2022 period, and documented null stop counts.

Summary

There is a 25 percentage-point spread in OTP between the best- and worst-served neighborhoods (all modes pooled). When restricted to bus-only, the spread narrows to 20 pp but the bottom neighborhoods remain the same. The disparity is structural and stable over time – all neighborhoods rise and fall together with the system. OTP is now computed from route-level averages (each route weighted once regardless of how many months of data it has), weighted by trip frequency.

Worst-Served Neighborhoods

The bottom neighborhoods are served entirely by bus, so their pooled and bus-only OTP are identical.

Best-Served Neighborhoods

Bus-Only Stratification (Simpson's Paradox Check)

Restricting to BUS-mode routes reveals that some neighborhoods' high pooled OTP is driven by rail:

Bon Air is a clear case of Simpson's paradox: it appears well-served in the pooled analysis (rank 13) but drops to rank 53 (bus-only) because its high pooled OTP is driven almost entirely by rail service. Beechview similarly drops 9 positions.

The bus-only spread (20 pp) is narrower than the pooled spread (25 pp), confirming that rail inflates the apparent equity of neighborhoods it serves.

Frequency-Weighting Effect

Comparing trip-weighted OTP to unweighted (equal weight per route) reveals where high-frequency service diverges from the route average:

• Mean gap: -0.27% (small on average – the two measures broadly agree).
• Range: -6.1% to +5.7% (meaningful divergence for individual neighborhoods).

• Negative gap (Carrick, Regent Square): high-frequency routes underperform relative to infrequent ones. Riders experience worse OTP than the simple route average suggests.
• Positive gap (Troy Hill): high-frequency routes are more reliable, so the rider experience is better than the route average implies.

Observations

• Best-performing neighborhoods are served by light rail (Overbrook, Beechview are on the T line) or short bus routes.
• Worst-performing neighborhoods depend on long local bus routes with many stops (e.g., routes 61C, 71B, 77).
• The quintile gap (Q5 - Q1) tracks roughly in parallel over time, meaning the equity disparity is baked into route structure rather than worsening.
• 89 neighborhoods analyzed; 3,760 of 6,466 stops were excluded because they lacked a neighborhood assignment in the data.
• Routes with fewer than 12 months of OTP data are excluded from the analysis.

Caveats

• Sample size varies widely: neighborhoods have between 1 and 74 routes. The 25 pp spread should be interpreted with this context – neighborhoods with only 1-2 routes have OTP estimates driven by a single route's performance, while those with 10+ routes have more stable estimates. A neighborhood served by one bad route will look worse than a neighborhood with a diversified mix.
• Panel balance (time series): The quintile time series uses an unbalanced panel. Neighborhoods gaining or losing routes over time may show OTP changes from composition shifts (a route entering or exiting), not performance changes. This could create artificial trends in the quintile chart, though the overall pattern of parallel movement suggests this effect is small.
• OTP is weighted by current trips_7d, not historical ridership. Neighborhoods where service was cut would show current-frequency weights, not past ones.
• The hood field had some invalid values (e.g., "0") that were filtered out.
• A neighborhood's OTP reflects the routes that pass through it, not the experience of residents who may transfer between routes.
• The unweighted measure treats each route equally regardless of how many trips it runs, which can overstate the importance of infrequent routes.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md — 7 issues (1 significant). Fixed time-pooled weighting (pre-aggregate OTP to route level before joining), added bus-only stratification revealing Simpson's paradox in Bon Air and Beechview, added NULL trips_7d filter, added minimum-month filter, documented panel balance caveat, added sample-size caveat, and clarified METHODS.md weighting description.

Summary

842 anomalous months were flagged across 94 routes using a rolling z-score method with a lagged window (current month excluded from the baseline). The detection is two-sided, flagging both sharp drops and spikes. Anomalies cluster in time (COVID, late 2022) rather than being randomly distributed, suggesting system-wide shocks.

Methodology Note

The anomaly detector uses a 12-month rolling window shifted by one month, so the current observation is never included in its own baseline. This prevents self-dampening of z-scores and produces more sensitive detection (842 anomalies vs. 406 with the unshifted approach). When the rolling standard deviation is near zero (constant OTP over the window), z-scores are set to 0.0 to avoid division-by-zero artifacts.

Routes with Most Anomalies

Anomaly Rates by Mode

RAIL routes show a slightly higher anomaly rate (14.3%) despite consistently high OTP. This is because their performance is normally very stable, so even moderate dips trigger the 2-sigma threshold. The 5 UNKNOWN-mode routes (RLSH, P2, 42, SWL, 37) are included in the analysis; most have very few months of data.

Expected vs Actual False-Positive Rate

With 7,076 evaluated route-month observations and a 2-sigma two-sided threshold, the expected false-positive rate under normality is approximately 4.6%, yielding ~322 expected false positives. The actual count of 842 anomalies is 2.6x the null expectation, indicating that a substantial majority of flagged anomalies reflect genuine OTP deviations beyond what random variation would produce. However, roughly 300-350 of the 842 could be expected by chance alone, so not every flagged anomaly should be interpreted as a "real" event.

Lagged-Window Trend Bias

The lagged rolling window introduces a systematic bias for trending routes. When a route's OTP is declining, the baseline (computed from the prior 12 months) is always slightly above the current value, making negative anomalies more likely. Conversely, improving routes are biased toward positive anomalies. This means the anomaly detector is more sensitive to deviations in the direction of the trend. No detrending is applied, so some fraction of flagged anomalies may reflect gradual trends rather than abrupt shocks.

Key Anomaly Clusters

• March–June 2020 (COVID): Many routes showed positive anomalies – OTP improved because reduced ridership meant less dwell time and fewer delays. This was a temporary artifact, not genuine improvement.
• Late 2022: A cluster of negative anomalies across many routes, coinciding with the system-wide OTP trough (58% in September 2022). May indicate staffing shortages, construction, or service restructuring.
• Route 79 (East Hills): The most anomaly-prone route, with 18 flagged months, indicating persistent instability in schedule adherence.

Excluded Routes

4 routes were excluded from anomaly detection because they have fewer than 7 months of data (the rolling window requires shift(1) + min_samples=6):

Observations

• The lagged window methodology results in more anomalies being flagged, particularly for routes with gradual trends, since the baseline is always slightly behind.
• Rail routes (RED, BLUE) have many anomalies despite high average OTP because their performance is normally very consistent, so even moderate dips trigger the 2-sigma threshold.
• The z-score method requires at least 6 months of rolling history, so the first few months of each route's data are not evaluated.
• 5 UNKNOWN-mode routes are included in the analysis (RLSH, P2, 42, SWL, 37). Most have very few months of data.

Caveats

• Without external data (PRT service advisories, construction records, staffing reports), anomalies can only be flagged, not explained.
• The known events dictionary is limited to COVID dates. More events could be added with PRT service change records.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md – 7 issues (1 significant). Added division-by-zero guard for z-scores, mode-stratified anomaly rates, false-positive rate context, trend bias documentation, excluded route documentation, two-sided detection clarification, and UNKNOWN-mode route documentation.

Summary

PRT shows a consistent seasonal cycle with winter months outperforming summer/fall. The system-wide seasonal swing is about 6.8 percentage points after detrending. 93 routes had sufficient data (3+ years) for route-level seasonal analysis.

System-Wide Seasonal Profile

Computed from a balanced panel of 93 routes (present in all 12 months-of-year) over complete calendar years (2019–2024).

Methodology Note

Seasonal profiles are computed by first removing a 12-month centered rolling mean (trend), then averaging the detrended residuals by month-of-year. This ensures that long-term trends (e.g., the COVID dip) do not distort the seasonal pattern. Route-level analysis requires at least 3 years of data to ensure each month-of-year is represented multiple times.

Red-team corrections applied (2026-02-10):

• Restricted to complete calendar years (2019-01 through 2024-12) to ensure every month-of-year has equal year coverage. Previously, December was missing 2025 data (the worst-performing year), inflating its seasonal average.
• Used a balanced panel of routes present in all 12 months-of-year for the system-wide profile. This excluded 5 routes: 3 winter-only routes with very high OTP (37 Castle Shannon 81%, 42 Potomac 83%, RLSH Red Line Shuttle 98%) and 2 with other gaps (53 Homestead Park, SWL). Their inclusion previously inflated winter averages.
• Note: trips_7d weighting is a static snapshot and may not reflect historical service levels. The seasonal pattern holds in both weighted and unweighted averages, so the core finding is robust to weighting choice.

Most Seasonally Affected Routes (detrended)

Observations

• The winter advantage is somewhat counterintuitive – one might expect snow and ice to worsen OTP. Possible explanations: lower ridership reduces dwell time; fewer construction detours; school breaks reduce congestion.
• September is consistently the worst month (-3.9 pp from trend), possibly due to the return of school-year traffic and late-summer construction.
• After applying the balanced panel filter and complete-years restriction, the seasonal pattern persists with minimal change in magnitude, confirming it is a genuine operational pattern rather than a data artifact.
• Most routes have a seasonal amplitude under 15%. The heatmap of the top 20 routes shows no single month dominates as "worst" across all routes – the pattern varies, though fall months are generally weaker.

Caveats

• Seasonal decomposition uses a centered moving-average method to remove trend, not a formal STL decomposition. Results are directionally correct but assume additive seasonality.
• Only 6 years of complete data (2019–2024) means each month-of-year average is based on ~6 detrended observations, limiting statistical power.
• The trips_7d weighting reflects a single point-in-time snapshot of service frequency, not historical values. Route frequencies likely changed over the study period (especially during COVID).

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analysis-06-seasonal-patterns.md — 4 issues (2 moderate). Balanced panel and complete-years restrictions applied; core finding confirmed.

Summary

There is a moderately strong negative correlation between the number of stops on a route and its average OTP. This finding holds for both all routes and bus-only analysis, ruling out Simpson's paradox as a confounder.

Key Numbers

• All routes: Pearson r = -0.53 (p < 0.001, n = 92)
• Bus only: Pearson r = -0.50 (p < 0.001, n = 89)
• Bus only: Spearman r = -0.49 (p < 0.001)
• Routes with < 50 stops: typically 80%+ OTP
• Routes with 150+ stops: typically below 60% OTP

Routes with fewer than 12 months of OTP data are excluded to avoid noisy averages from sparse observations.

Observations

• The bus-only correlation (r = -0.50) is nearly as strong as the all-routes correlation (r = -0.53), confirming that the effect is not driven by the BUS/RAIL mode split (Simpson's paradox). Stop count predicts OTP within the bus mode alone.
• The Spearman rank correlation (r = -0.49) is consistent with the Pearson, indicating the relationship is approximately monotonic without being driven by outliers or non-linearity.
• Every stop adds dwell time (boarding/alighting), traffic signal delay, and schedule recovery risk. The cumulative effect is substantial.
• Busway and rail routes tend to have fewer stops and dedicated right-of-way, giving them a double advantage.
• Route 77 (Penn Hills) is an extreme case: 258 stops and among the worst OTP in the system.

Implication

Stop consolidation – reducing the number of stops on long routes – is a common transit strategy for improving schedule adherence. This data strongly supports that approach for PRT's worst-performing routes.

Caveats

• Correlation is not causation. Routes with many stops also tend to serve congested corridors, cover longer distances, and carry more passengers – all of which independently affect OTP.
• Temporal mismatch: Stop counts come from the current route_stops snapshot while OTP is averaged across all historical months (2019–2025). Routes that changed stop configurations during this period have a mismatch between their current stop count and earlier OTP observations. This is inherent to the available data and cannot be corrected without historical stop-count snapshots.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md — 6 issues (0 significant). Added 12-month minimum filter, temporal mismatch note in METHODS.md, all_n tracking, replaced manual regression with linregress, added min-n guard, updated METHODS.md for Pearson+Spearman.

Important: Derived Metric

Stop-level OTP is a derived metric: each stop inherits the average OTP of the routes serving it, weighted by trip frequency (trips_7d). It reflects route composition at each stop, not independently measured stop-level performance. A stop served by a single high-OTP route will appear "high-performing" even if that stop is a chronic delay point on that route. Conversely, a stop served by many routes will reflect the blended average of those routes.

Summary

6,212 stops were mapped with route-weighted OTP (after excluding 2 stops with null/NaN OTP due to zero total trips, and excluding routes with fewer than 12 months of data). Poor performance clusters in eastern Pittsburgh (Penn Hills, Squirrel Hill, Highland Park), while the best performance follows the light rail and busway corridors.

Geographic Patterns

• Best corridors: The light rail T line (Beechview/Overbrook south to Library) and the East Busway (Wilkinsburg to downtown) form clear green bands on the map, with 80%+ OTP at most stops.
• Worst corridors: Eastern neighborhoods served by Route 77 (Penn Hills) show the lowest stop-level OTP at 55.8%. The 61-series routes through McKeesport and Homestead also form a low-OTP cluster.
• Downtown: Mixed performance. Stops in the Golden Triangle are served by many routes, so their weighted OTP reflects the system average (~65–70%).

Mode Context

The best-performing stops (88.4%) are all served exclusively by BUS routes – specifically Route 18 (Manchester). The high-OTP corridor along the T line reflects rail's structural advantage (dedicated right-of-way), not independently measured stop performance. When interpreting the map:

• Rail stops (light rail T line) appear green primarily because RAIL routes average ~84% OTP system-wide. These stops' high performance reflects mode advantage, not stop-specific factors.
• Busway stops (East Busway, West Busway) also appear green for similar reasons – dedicated right-of-way.
• Genuinely high-performing bus stops include those on Route 18 (Manchester, 88.4%) and Route 39 (Brookline), which achieve high OTP on mixed-traffic streets.

Observations

• The worst-performing stops (55.8%) are exclusively served by Route 77, the system's lowest-ranked route.
• The best-performing stops (88.4%) are exclusively served by Route 18 (Manchester) – a bus route, not rail.
• Stops served by multiple routes tend toward the system mean, since the weighting blends good and bad routes.
• The system average displayed in the chart title (unweighted stop-level average) treats every stop equally regardless of trip volume. A trip-weighted system average would differ slightly.

Caveats

• The map uses a simple lat/lon scatter, not a true geographic projection. At Pittsburgh's latitude, this introduces minor distortion but the overall shape is recognizable.
• Stops with null or NaN OTP values (2 stops) were excluded from the map.
• OTP is averaged across all months (2019–2025), so the map doesn't show temporal changes.
• Routes with fewer than 12 months of OTP data were excluded to avoid projecting noisy estimates onto the map.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md – 7 issues (1 significant). Documented derived-metric nature of stop OTP, added mode column and bus/rail context, added minimum 12-month filter for route OTP, clarified unweighted system average, corrected NaN claim, fixed hood="0" sentinel, added dropped-stop logging.

Summary

The Monongahela Incline is a data pipeline artifact. It appears in the route catalog but has zero OTP measurements. OTP was never recorded for either of Pittsburgh's two inclines.

What the Data Shows

Observations

• Both the Monongahela Incline (MI) and the Duquesne Incline (DQI) exist in the routes table with mode=INCLINE, but neither has any OTP data.
• The inclines are physically operational and appear in PRT's GTFS feed with regular service (78 weekday trips).
• The OTP measurement system (whatever generates routes_by_month.csv) simply does not cover incline routes. This is likely because inclines run on a fixed schedule with no traffic interference, making OTP measurement less meaningful.
• The ANALYSIS-PROPOSAL.md described this as "zero values" – in fact, there are no values at all, not even zeros.

Conclusion

This is not a data quality issue to fix. The inclines were included in the route catalog because they're part of PRT's GTFS feed, but were excluded from OTP measurement, likely by design. No further action needed.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md — 3 issues (0 significant). Expanded OTP query to explicitly check both MI and DQI (substantiating the claim that neither incline has data), updated METHODS.md question wording.

Summary

There is no meaningful correlation between peak weekday trip frequency and OTP. The previous finding (r = -0.39) was an artifact of using SUM(trips_wd) across stops, which conflated frequency with route length. After correcting to MAX(trips_wd) (peak frequency at any single stop), the correlation vanishes.

Key Numbers

• All routes: Pearson r = 0.03 (p = 0.81, n = 92) – essentially zero
• Bus only: Pearson r = -0.06 (p = 0.55, n = 89)
• Bus only: Spearman r = -0.11 (p = 0.29)

Methodology Note

The original analysis summed trips_wd across all stops on a route. Because trips_wd is recorded per stop, a route with 50 trips per day and 100 stops produces a sum of ~5,000, while a route with 50 trips per day and 20 stops produces ~1,000. This made the metric a proxy for frequency x stop_count rather than pure frequency. Using MAX(trips_wd) isolates the peak trip frequency at the busiest stop, which is a better measure of how often the route actually runs.

Observations

• Running more trips per se does not degrade OTP. The previous apparent correlation was entirely driven by the confounding of frequency with route length (stop count).
• This result is consistent with Analysis 07's finding that stop count is the real structural predictor – once route complexity is removed from the frequency metric, the effect disappears.
• Some of the highest-frequency routes (P1 East Busway, RAIL lines) actually have excellent OTP, because they combine high frequency with few stops and dedicated right-of-way.

Implication

PRT should not expect OTP penalties from increasing service frequency on existing routes. The capacity to run more trips does not inherently strain schedule adherence. The real lever for improving OTP is route design (stop count, right-of-way), not service volume.

Caveats

• trips_wd in route_stops represents current weekday frequency, not historical. Frequency may have changed over the analysis period.
• MAX(trips_wd) captures the peak stop, which for short-turn routes may overstate the frequency experienced by riders at outer stops.
• Routes with fewer than 12 months of OTP data are excluded (1 route dropped vs prior version).
• Three correlation tests were run (Pearson all-routes, Pearson bus-only, Spearman bus-only) without multiple-comparison correction. Since all three are non-significant (smallest p = 0.29), correction would not change any conclusion.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md – 6 issues (1 significant). Updated METHODS.md to reflect MAX(trips_wd) instead of SUM; documented all three correlation tests; added minimum-month filter (HAVING COUNT >= 12); added NULL filter for trips_wd; replaced manual regression with scipy.stats.linregress; noted multiple-test caveat.

Summary

The correlation between directional trip imbalance and OTP is weak and not statistically significant (r = -0.12, p = 0.26). After correcting methodology issues in the original analysis, PRT routes show very little directional asymmetry, and what asymmetry exists does not predict OTP.

Key Numbers

• All routes: Pearson r = -0.12 (p = 0.26, n = 90)
• Bus only: Pearson r = -0.12 (p = 0.28, n = 87)
• Bus only: Spearman r = -0.17 (p = 0.11)
• Maximum asymmetry index: 0.077 (Route 19L)

Methodology Note

The original analysis used SUM(trips_wd) per direction and excluded stops with direction = 'IB,OB'. This inflated asymmetry because IB,OB stops (common on shared corridors) were dropped rather than counted in both directions. Routes 11 and 60 appeared 100% asymmetric because their IB stops were all coded as IB,OB. The corrected analysis uses MAX(trips_wd) per direction (peak frequency, not total stop-visits), includes IB,OB stops in both directions, and excludes routes present in only one direction.

Most Asymmetric Routes

Observations

• With corrected methodology, PRT routes are remarkably balanced directionally. The most asymmetric route (19L) has only a 7.7% imbalance (7 vs 6 trips), and most routes are at or near 0%.
• The previous finding of routes with 100% asymmetry (Routes 11 and 60) was a data artifact caused by excluding bidirectional (IB,OB) stops. These routes are excluded in the corrected analysis because they lack separate IB and OB data after the fix.
• The slight negative correlation (r = -0.12) suggests marginally worse OTP with more asymmetry, but the effect is too small and not statistically significant.

Conclusion

Directional imbalance does not predict OTP. PRT routes are sufficiently balanced that this is not a measurable factor in schedule adherence. The hypothesis that scheduling asymmetry creates operational strain is not supported by this data.

Caveats

• The analysis uses peak trip frequency (MAX(trips_wd)) at a single stop per direction, which may not capture all scheduling nuances.
• The route_stops data reflects current service, not historical. Historical asymmetry may have differed.
• Including IB,OB stops in both directions can compress the asymmetry index toward zero when an IB,OB stop has the highest trips_wd for a route. In that case, both IB and OB MAX values equal the same number, mechanically forcing asymmetry to zero. This is a known limitation – the alternative (excluding IB,OB stops) creates the opposite bias by dropping data.
• Routes with fewer than 12 months of OTP data are excluded.
• Three correlation tests were run (Pearson all-routes, Pearson bus-only, Spearman bus-only) without multiple-comparison correction. Since all three are non-significant (smallest p = 0.11), correction would not change any conclusion.

Review History

• 2026-02-11: RED-TEAM-REPORTS/2026-02-11-analyses-01-05-07-11.md – 7 issues (1 significant). Updated METHODS.md to correctly describe IB,OB handling (include in both, not exclude); corrected "total trips" to "peak frequency (MAX)"; added minimum-month filter (HAVING COUNT >= 12); added NULL filter for trips_wd; replaced manual regression with scipy.stats.linregress; documented IB,OB compression effect; noted multiple-test caveat.

Summary

Geographic span (the maximum distance between any two stops on a route) is a moderate negative predictor of OTP within bus routes (r = -0.38, p < 0.001), but stop count remains the stronger predictor after controlling for the other. Partial correlation analysis disentangles the two: stop count predicts OTP even after controlling for span (partial r = -0.41, p < 0.001), while span's independent contribution is smaller (partial r = -0.23, p = 0.03).

Key Numbers

• Span vs OTP (bus only, primary): Pearson r = -0.38 (p < 0.001, n = 89), Spearman rho = -0.37 (p < 0.001)
• Span vs OTP (all routes, secondary): r = -0.32 (p = 0.002, n = 92) – includes Simpson's paradox risk
• Stop density vs OTP (bus only): r = 0.04 (p = 0.71) – not significant
• Span vs OTP | stop count (bus, partial): r = -0.23 (p = 0.03)
• Stop count vs OTP | span (bus, partial): r = -0.41 (p < 0.001)
• Span-stop count collinearity: r = 0.41

Observations

• The bus-only correlation (r = -0.38) is actually stronger than the all-mode correlation (r = -0.32). The pooled-mode result was muted by Simpson's paradox – rail routes have moderate span but high OTP, pulling the all-mode trend line toward zero.
• Span and stop count are moderately correlated (r = 0.41), but not so strongly as to make partial correlation unreliable.
• After controlling for stop count, span still has a small but significant independent effect – longer routes face additional challenges beyond just having more stops (longer exposure to traffic, more variance in conditions).
• However, stop count's partial correlation (-0.41) is nearly twice span's (-0.23), confirming that the number of stops matters more than the distance covered.
• Stop density (stops per km) shows no correlation with OTP at all (r = 0.04), meaning that tightly-packed stops are no worse than widely-spaced stops once total count and distance are accounted for.

Implication

Both stop count and route distance independently degrade OTP, but stop consolidation is the higher-leverage intervention. Shortening routes would help modestly, but eliminating stops on existing routes would have roughly twice the impact per unit of change.

Caveats

• Geographic span (max pairwise distance) is a crude proxy for actual route length. GTFS shape data would provide a more accurate route-length measurement.
• Routes with fewer than 12 months of data are excluded to reduce noise.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 4 issues (1 significant). Bus-only correlations now primary; Spearman added.

Summary

After detrending (subtracting system-wide monthly mean OTP), hierarchical clustering on pairwise OTP correlations produced 6 clusters (selected by silhouette score optimization). Detrending removes the dominant COVID/seasonal signal that otherwise causes all routes to appear positively correlated, revealing genuine differential behavior.

Key Numbers

• Silhouette scores ranged from 0.13 to 0.18 (k=6 was optimal at 0.178)
• 0 route pairs excluded for insufficient overlap

Methodology

• Detrending: System-wide monthly mean OTP is subtracted from each route's OTP before computing correlations. This ensures clusters reflect differential route behavior rather than common system-wide trends (COVID, seasonal cycles).
• Linkage: Average linkage (valid for non-Euclidean correlation distance), replacing the original Ward's method.
• Cluster count: Selected by silhouette score optimization over k=3..10, replacing the hardcoded k=6.
• Imputation: Route pairs with insufficient overlap are imputed with median correlation rather than 0.0.

Observations

• With detrending, the clusters are more evenly sized and differentiated by OTP level.
• The highest stop-count cluster (Cluster 6, 146 avg stops) does not have the worst OTP (68.9%), suggesting that after removing system-wide trends, route complexity alone doesn't determine co-movement.
• Low silhouette scores (0.13-0.18) indicate moderate cluster separation – routes don't form tightly distinct groups. This is expected given that detrended OTP residuals have limited signal.
• Without depot or corridor data, the clusters remain descriptive – we can see which routes move together but cannot explain why.

Caveats

• Silhouette scores below 0.25 indicate weak cluster structure. The 6-cluster solution is the best available, but route co-movement may be more continuous than discrete.
• All modes are pooled. With only ~3 rail routes, stratification by mode is not feasible.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 5 issues (2 significant). Detrended correlations, average linkage, silhouette-based k selection; cluster composition changed entirely.

Summary

The system-wide OTP decline since COVID is unevenly distributed. Of 92 routes with data in both periods, 43 improved and 49 declined, with a median delta of -0.9 pp and a mean delta of -2.1 pp. However, a significant regression-to-the-mean effect (r = -0.25, p = 0.02) means that much of the apparent divergence between "improved" and "declined" routes is a statistical artifact: routes with extreme baselines naturally regress toward the mean.

Key Numbers

• 92 routes with data in both pre-COVID (2019-01 to 2020-02) and current (2024-12 to 2025-11) periods
• 43 improved, 49 declined
• Median recovery delta: -0.9 pp
• Mean recovery delta: -2.1 pp
• Regression-to-the-mean: r = -0.25 (p = 0.02) – routes with high baselines tended to decline; routes with low baselines tended to improve
• Kruskal-Wallis test across subtypes: H = 5.5, p = 0.24 – no significant difference between route types
• Stop count vs recovery (bus): r = -0.11, p = 0.32 – not significant

Most Improved / Most Declined

Most improved:

Most declined:

Observations

• The regression-to-the-mean test is significant (r = -0.25, p = 0.02): routes that started with below-average OTP tended to improve, and routes that started above-average tended to decline. This does not mean the recovery differences are entirely artifactual, but it means the extreme cases (P7 improving +17 pp from a 58.7% baseline, or Route 6 declining -17.8 pp from an 80.5% baseline) are partially explained by statistical regression rather than operational changes.
• The Kruskal-Wallis test across subtypes is not significant (p = 0.24), meaning there is no statistically defensible evidence that premium routes recovered better than local routes as a group. The observation that the top improvers are flyers/busway routes may reflect cherry-picking the extremes rather than a systematic pattern.
• That said, the most-declined routes are genuinely concentrated in Pittsburgh's eastern neighborhoods (Highland Park, Greenfield, Squirrel Hill), and these declines are large enough to be concerning regardless of the RTM effect.

Implication

The recovery picture is more nuanced than "premium routes improved, local routes declined." RTM explains a substantial fraction of the divergence. The policy-relevant finding is narrower: specific local bus routes in the eastern corridor have deteriorated badly (15-21 pp below pre-COVID levels), and this decline exceeds what RTM alone would predict.

Caveats

• Regression to the mean is not the only explanation. Operational changes (schedule modifications, staffing shifts) may have genuinely affected some routes more than others.
• The current period is the trailing 12 months of available data (2024-12 to 2025-11), which may not represent a stable equilibrium.
• The pre-COVID baseline (2019-01 to 2020-02) includes months of varying performance; a longer baseline would be more stable.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 3 issues (2 significant). RTM test and Kruskal-Wallis added; "premium routes recovered better" claim narrowed.

Summary

81 municipalities had enough stops (10+) to analyze. There is a 25 pp spread between the best and worst municipalities, similar to the neighborhood-level equity gap. Cross-jurisdictional routes (serving 2+ municipalities) perform no differently from single-municipality routes.

Key Numbers

• 81 municipalities analyzed (with much better data coverage than the 89 neighborhoods in Analysis 04)
• Best: Castle Shannon borough (84.0%)
• Worst: Plum borough (59.1%)
• Spread: 24.9 pp
• Suburban median OTP: 68.1%
• Cross-jurisdictional routes (n=74): avg OTP = 69.5%
• Single-municipality routes (n=19): avg OTP = 69.2%
• Cross vs single t-test: p = 0.85 – no significant difference

Observations

• The best-performing municipalities (Castle Shannon, Dormont, Beechview) are all served by the light rail T line, consistent with the mode advantage found in Analysis 02.
• The worst-performing municipalities (Plum, Penn Hills, Wilkinsburg) are served primarily by long local bus routes through the eastern corridor.
• The suburban median OTP (68.1%) is very close to the overall system average, suggesting no systematic suburban vs urban disadvantage.
• Cross-jurisdictional routes – which might be expected to suffer from longer distances and more complexity – perform identically to single-municipality routes. Route length and stop count matter more than jurisdictional boundaries.
• The municipal analysis has much better data coverage than the neighborhood analysis (Analysis 04), which lost 58% of stops due to missing hood data.

Implication

The equity gap is driven by mode and route structure, not by geography per se. Municipalities on rail or busway corridors get 80%+ OTP; those served only by long local bus routes get 60%. Municipal boundaries and suburban/urban distinctions are not meaningful predictors.

Caveats

• Route OTP is projected onto stops and then onto municipalities (ecological fallacy). A route's performance may vary along its length, and municipalities at the ends of long routes may experience different OTP than those near the middle.
• Trip weights (trips_7d) are a static snapshot applied across the full study period. Service levels changed over time, especially during COVID.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 3 issues (2 significant, inherent to data). Ecological fallacy documented; Welch's t-test applied (no material change).

Summary

Higher-connectivity stops appear to have modestly worse OTP in stop-level data, but this finding does not survive correction for non-independence. At the route level (independent observations), the correlation between stop connectivity and OTP is not significant (r = -0.15, p = 0.16). The apparent "hub penalty" is a composition effect driven by inflated sample size at the stop level.

Key Numbers

Stop-level (n=6,209 – non-independent, inflated power):

• Pearson r = -0.17 (p < 0.001)
• Spearman rho = -0.32 (p < 0.001)

Route-level (n=93 – independent observations):

• Pearson r = -0.15 (p = 0.16)

Route-level, bus only (n=90):

• Pearson r = -0.09 (p = 0.39)

Observations

• The stop-level correlations (r = -0.17, rho = -0.32) are statistically significant but misleading: the 6,209 "stops" are not independent observations. Stops on the same route share the same underlying OTP, so the effective sample size is closer to ~90 (the number of distinct routes). With n_eff ~ 90, a correlation of r = -0.15 yields p = 0.16, which is not significant.
• The route-level analysis confirms this: average stop connectivity per route has no significant relationship with route OTP (r = -0.15, p = 0.16). Within bus routes only, the relationship is even weaker (r = -0.09, p = 0.39).
• The 3.5 pp tier gap (simple 69.5% vs hub 66.4%) is real in the raw data but reflects a composition effect: hubs are served by many routes including poor-performing local bus routes, which drag down the average. The hub location itself is not causing worse OTP.
• The busiest hub (East Busway Penn Station, 27 routes) actually outperforms the system average (72.1%) because it sits on dedicated right-of-way.

Implication

Being a transfer hub does not independently predict worse OTP. The apparent hub penalty is driven by which routes converge there. Policy should focus on improving the poorly-performing routes themselves, not on the hub locations.

Caveats

• This analysis uses route-level OTP projected onto stops (ecological fallacy). We don't have stop-level OTP data; a route's on-time performance may vary along its length.
• The route-level analysis uses "average stop connectivity per route," which is itself an approximation. A more direct test would require stop-level arrival data.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 3 issues (2 significant). "Hub penalty" finding retracted; route-level analysis now primary.

Summary

There is no meaningful correlation between a route's weekend-to-weekday service ratio and its OTP. Routes that run heavy weekend service perform identically to commuter-oriented weekday-heavy routes.

Key Numbers

• Pearson r = -0.03 (p = 0.79, n = 93)
• Spearman rho = -0.02 (p = 0.84)

Observations

• The three service tiers are virtually indistinguishable in OTP (69.8%, 68.8%, 70.3%).
• Neither Pearson nor Spearman correlations approach significance.
• This null result makes sense: the weekend service ratio reflects demand patterns and scheduling choices, not route structure. A route with high weekend service isn't inherently harder to run on time.
• Since OTP is reported monthly (not by day-of-week), it aggregates weekday and weekend performance, which may mask day-specific patterns.
• Bus-only correlation (r = -0.06, p = 0.56) confirms the null result holds within the dominant mode.

Implication

Weekend vs weekday service intensity is not a useful predictor of OTP. The structural factors identified in other analyses (stop count, mode, route length) dominate.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 2 issues (both moderate). Bus-only correlation added; caveats strengthened. Null finding unchanged.

Summary

A six-feature OLS model explains 47.2% of OTP variance (adjusted R² = 0.435) across 92 routes. Three features are significant: stop count, geographic span, and rail mode. The model confirms that structural route characteristics explain nearly half of all performance variation, with the remaining 53% attributable to unmeasured factors (traffic, staffing, weather, schedule design).

Key Numbers

• R² = 0.472, Adjusted R² = 0.435
• n = 92 routes, k = 6 features

Observations

• Stop count (beta = -0.49) and geographic span (beta = -0.47) are the two strongest predictors, with nearly equal standardized effects. Each additional stop costs roughly -0.06 pp OTP; each additional km of span costs roughly -0.49 pp.
• Rail mode (beta = +0.34) provides a +13.3 pp OTP advantage over bus after controlling for structural factors. This is partly inherent to rail (dedicated right-of-way) and not fully captured by other features.
• Number of municipalities has a surprising positive coefficient (+0.009 per muni, beta = +0.41). This is likely a suppressor effect: after controlling for stop count and span, routes that serve more municipalities tend to be express/busway routes that skip stops, which perform better.
• Premium bus (busway/flyer/express/limited) is not significant once stop count and span are controlled – these routes' advantage is fully explained by having fewer stops and shorter spans, not by their service type per se.
• Weekend ratio is not significant, confirming the null finding from Analysis 17.

Model Interpretation

The 47% R² means that knowing just a route's stop count, length, and mode gets you almost halfway to predicting its OTP. The unexplained 53% likely reflects:

• Traffic conditions and road geometry
• Schedule design (running time padding, layover adequacy)
• Driver staffing and experience
• Passenger volume and dwell time variation
• Weather and construction effects

These factors would require operational data not present in this dataset.

Caveats

• OLS assumes linear relationships and independent errors. Some non-linearity is visible in the residuals.
• The n_munis coefficient is a suppressor and should not be interpreted as "more municipalities = better OTP."
• With only 92 observations and 6 predictors, the model is at the edge of stable estimation.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 4 issues (3 significant). VIF check added; n_munis labeled as suppressor; numerical stability improved.

Summary

Ridership-weighted system OTP (69.4%) runs 1.6 percentage points higher than trip-weighted OTP (67.8%), and the difference is statistically significant (paired t = -18.1, p < 0.001; Wilcoxon W = 1, p < 0.001). This means the average PRT rider experiences slightly better on-time performance than the trip-weighted system average suggests.

Key Numbers

• Unweighted OTP (all routes equal): 69.9% mean, 70.3% median
• Trip-weighted OTP (scheduled frequency): 67.8% mean, 67.8% median
• Ridership-weighted OTP (avg daily riders): 69.4% mean, 69.2% median
• Ridership vs trip-weighted gap: +1.6 pp (p < 0.001, n = 70 months)
• 93 routes with 12+ months of paired OTP + ridership data
• Overlap period: Jan 2019 – Oct 2024 (70 months)

Interpretation

Both weighted series fall below the unweighted average, meaning both scheduled trips and actual riders concentrate somewhat on worse-performing routes. However, trip frequency overstates how much ridership is concentrated on the worst routes. High-frequency routes tend to have many stops and poor OTP (Analysis 07), but riders don't fill those trips proportionally – some high-frequency routes carry fewer riders per trip than expected. The result is that the average rider's experience is worse than the average route's OTP, but not as bad as the trip-weighted number implies.

This does not mean high-ridership routes have better OTP. It means ridership is distributed more evenly across the OTP spectrum than trip frequency is.

Observations

• The gap between trip-weighted and ridership-weighted OTP is not constant: it was near zero during COVID (2020), widened to ~3 pp in late 2022, and has stabilized around 1–2 pp since 2023. This likely reflects post-COVID ridership redistribution.
• All three series show the same overall trend: COVID spike, steady decline through late 2022, partial stabilization in 2023–2024.

Caveats

• Ridership data is weekday average only; the analysis does not capture weekend rider experience.
• route_stops.trips_7d is a current snapshot, not a monthly time series – trip-weighted OTP uses the same weights for all months.
• Routes missing from the ridership dataset (RLSH, SWL) are excluded from all three series for comparability, so the unweighted series here may differ slightly from Analysis 01.
• The ridership CSV ends Oct 2024 while OTP data extends to Nov 2025; the analysis is restricted to the overlap period.

Summary

There is no evidence that OTP declines predict subsequent ridership losses. After detrending and Bonferroni correction, zero of 93 routes show statistically significant Granger causality from OTP to ridership. The raw cross-correlations are weakly negative, suggesting the opposite direction: months with lower ridership tend to have better OTP.

Key Numbers

• Granger causality: 8/93 routes significant at p < 0.05 uncorrected; 0/93 after Bonferroni correction
• Median cross-correlation at lag 0: r = -0.18 (IQR: [-0.41, +0.10])
• Median cross-correlation at lag 1: r = -0.15 (IQR: [-0.38, +0.09])
• Cross-correlations are flat across lags 0–6 – no dominant lag emerges
• 93 routes with 36+ months of paired OTP + ridership data (57–70 months each)
• Both series detrended by subtracting system-wide monthly mean before testing

Observations

• The p-value histogram is roughly uniform (with a small pile-up near zero), consistent with the null hypothesis being true for most routes.
• Of the 8 nominally significant routes, 3 have best lag = 1 month and the rest are scattered across lags 2–6. No consistent lag structure emerges.
• The weakly negative contemporaneous correlation (median r = -0.18) is consistent with reverse causality: months when fewer people ride (summer, holidays) see better OTP because of reduced dwell times and less crowding, not because good OTP attracts riders.

Discussion

The hypothesis that poor OTP drives riders away is intuitive, but this data cannot confirm it. Several factors may explain the null result:

• Temporal resolution is too coarse: monthly data may be too slow to capture rider responses, which could operate at the trip or week level.
• Riders have limited alternatives: in a single-provider transit system, riders may tolerate poor OTP because they have no substitute, especially for commute trips.
• Confounders dominate: ridership is driven primarily by employment, gas prices, weather, and COVID – factors far larger than OTP fluctuations. The detrending removes system-wide trends but not route-specific confounders.
• Reverse causality may mask the effect: if high ridership causes poor OTP (crowding, dwell times) while poor OTP also causes ridership loss, the two effects partially cancel.

Caveats

• Granger causality tests linear predictive ability, not true causation. A null result does not prove OTP has no effect on ridership.
• The 70-month overlap period with monthly granularity gives limited statistical power for 6-lag models (effective sample ~60 per route).
• Detrending removes system-wide trends but not route-specific shocks (e.g., service changes, construction).
• Bonferroni correction is conservative; a less strict correction (e.g., Benjamini-Hochberg) might yield a few significant routes, but the overall pattern would remain weak.

Summary

Zero of 93 routes have recovered to pre-COVID ridership levels (median -43%, all negative). Routes that lost more ridership tended to see better OTP recovery (r = -0.21, p = 0.047), weakly supporting the hypothesis that ridership recovery degrades OTP through crowding and longer dwell times.

Key Numbers

• Ridership recovery: median -43.4%, mean -44.5%; 0/93 routes at or above pre-COVID
• OTP recovery: 35/93 routes improved, 58/93 declined vs pre-COVID
• Correlation (ridership change vs OTP change): Pearson r = -0.21, p = 0.047; Spearman r = -0.29, p = 0.005
• Kruskal-Wallis (OTP delta by subtype): H = 2.89, p = 0.58 (not significant)
• Pre-COVID baseline: Jan 2019 – Feb 2020; recovery period: Jan 2023 – Oct 2024
• 93 routes with 6+ months in both periods

Observations

• The scatter plot falls entirely in the left half (all ridership declines). The two populated quadrants are "both declined" (58 routes) and "riders down, OTP up" (35 routes). There are zero routes in the "both improved" or "riders up, OTP down" quadrants.
• Flyers lost the most ridership (median -68%), consistent with the collapse of peak-hour commute demand. Despite this, flyers show the widest spread in OTP recovery (some improved substantially, others declined).
• Busway routes had the best OTP recovery (median +3.3 pp), likely because their dedicated right-of-way insulates them from the traffic impacts that affect other routes.
• Local bus routes (n=64) show the widest spread on both axes, reflecting the diversity of the category. Some locals improved OTP by 10 pp while others declined by 19 pp.
• The routes that improved OTP the most (P7 +18 pp, P69 +10 pp, 41 +10 pp) all lost substantial ridership (-32% to -61%), consistent with the idea that fewer riders means shorter dwell times and better schedule adherence.

Discussion

The weak negative correlation between ridership recovery and OTP recovery is consistent with a crowding mechanism: routes that regained more riders saw their OTP degrade (or fail to improve), while routes that stayed emptier ran closer to schedule. However, the effect is weak (r = -0.21) and the correlation is borderline significant (p = 0.047), so it should be interpreted cautiously.

The most policy-relevant finding is the universal ridership collapse: every single route is still below pre-COVID levels, with a median loss of 43%. This dwarfs any OTP effects. The system is running fewer riders on roughly the same infrastructure, and OTP has still declined for most routes – suggesting that the OTP decline is driven by operational factors (staffing, vehicle maintenance, traffic congestion) rather than demand-side crowding alone.

The absence of subtype differences (Kruskal-Wallis p = 0.58) confirms Analysis 14's finding: no route type has recovered OTP systematically better or worse than others.

Caveats

• The ridership data ends Oct 2024; more recent ridership trends are not captured.
• "Recovery" is defined as a simple average comparison between two periods, not a trajectory analysis. A route could be on an upward trend that the period average does not fully reflect.
• The correlation between ridership change and OTP change does not establish causation; both could be driven by a third factor (e.g., service cuts, schedule changes).
• Flyer and busway subtypes have small sample sizes (n=17 and n=3), limiting subtype-level conclusions.
• Ridership data is weekday only; weekend recovery patterns may differ.

Summary

Over the Jan 2019 – Oct 2024 overlap period, PRT accumulated 55.5 million late weekday rider-trips out of 179.2 million total (31% late rate). The top 10 routes by delay burden account for 26.6% of all late rider-trips, and ridership weighting substantially reshuffles which routes appear most problematic compared to a pure OTP ranking.

Key Numbers

• 55.5 million cumulative late weekday rider-trips (Jan 2019 – Oct 2024)
• 179.2 million total weekday rider-trips; 31.0% system late rate
• Top 10 routes account for 26.6% of all late rider-trips
• Rank correlation between OTP rank and burden rank: Spearman r = 0.40 (p < 0.001) – moderate, meaning ridership significantly reshuffles priorities
• 93 routes with paired OTP + ridership data

Top 10 Routes by Delay Burden

Route 51 (Carrick) is the standout example: it ranks only 55th by OTP (68.6%, near the system average) but 2nd by delay burden because it carries massive ridership. Conversely, Route 77 (Penn Hills) has the worst OTP (54.9%) but ranks only 18th by burden because fewer people ride it.

Observations

• Ridership dramatically reshuffles priorities. The Spearman rank correlation between OTP rank and burden rank is only 0.40 – OTP rank alone is a poor proxy for human impact.
• The biggest upward shifts (more burden than OTP suggests) are high-ridership transit routes: P1 East Busway (+77 ranks), RED light rail (+72), BLUE light rail (+65). These routes have decent OTP (80%+) but carry so many riders that even their small late fractions generate substantial burden.
• The biggest downward shifts (less burden than OTP suggests) are low-ridership flyers: 65 Squirrel Hill (-70), P69 Trafford Flyer (-66), P13 Mount Royal Flyer (-51). These have poor OTP but few riders, so the total human impact is small.
• The delay burden trend shows a sharp drop during COVID (1.5M to 0.3M monthly late rider-trips), then a partial recovery to ~0.8-1.0M by 2024 – still well below pre-COVID levels primarily because ridership hasn't recovered.
• Pre-COVID, the system averaged ~1.3M late rider-trips per month. Post-COVID (2023-2024), it averages ~0.8M – a 40% reduction driven almost entirely by ridership collapse, not OTP improvement.

Discussion

This analysis reframes the OTP problem from "which routes are most unreliable" to "where does unreliability affect the most people." The two questions give different answers. A policy intervention on Route 51 (the #2 burden route) would affect more riders than fixing Route 77 (the #1 worst OTP route), even though 51's OTP is 14 pp better. Similarly, even small OTP improvements on high-ridership rail/busway routes would reduce more late rider-trips than large OTP improvements on low-ridership flyers.

The system's total delay burden has paradoxically decreased post-COVID – not because service improved, but because fewer people are riding. If ridership recovers without OTP improvements, the burden will return to or exceed pre-COVID levels.

Caveats

• "Late rider-trips" is a derived metric: avg_riders day_count (1 - OTP). It does not measure actual delay duration – a trip that is 1 minute late counts the same as one that is 30 minutes late.
• Ridership data is weekday only; weekend burden is not captured.
• OTP is a route-level monthly average; stop-level or trip-level variation is not reflected.
• The metric assumes all riders on a route experience the same OTP, which is an approximation – riders at different stops on the same route may have different experiences.

Summary

PRT garages differ significantly in route-level OTP, and the difference survives controlling for route structure. An OLS model with stop count and geographic span as controls shows that garage dummies add significant explanatory power (F = 4.55, p = 0.005). Collier garage routes run +5.4 pp above East Liberty routes after controlling for stop count and span (p < 0.001).

Key Numbers

• Kruskal-Wallis (all routes): H = 24.4, p = 0.0001 (5 garages)
• Kruskal-Wallis (bus only): H = 20.0, p = 0.0002 (4 garages)
• 93 routes with 12+ months of paired data

Controlled OLS Model (bus only, n = 89, reference = East Liberty)

F-test for garage dummies: F = 4.55, p = 0.005 – garages are significant after controls.

Observations

• Collier routes outperform East Liberty by +5.4 pp even after controlling for stop count and span (p < 0.001). This is a substantial and statistically robust effect.
• Ross routes outperform East Liberty by +2.9 pp after controls (p = 0.04), a marginally significant effect.
• West Mifflin does not differ significantly from East Liberty after controls (+1.4 pp, p = 0.36). The raw difference between these two garages (0.8 pp) was largely explained by route structure.
• Adding garage dummies increases R² from 0.313 to 0.410 (+9.7 pp), a meaningful improvement beyond what route structure alone explains.
• The monthly trend chart shows all garages move together with system-wide trends (COVID spike, 2022 trough), but the relative ordering is stable: Collier consistently above Ross, which is consistently above East Liberty and West Mifflin.

Discussion

The controlled analysis overturns the initial interpretation that garage differences were purely a composition effect. Collier's advantage is real and operationally meaningful: after accounting for the fact that it operates shorter routes with fewer stops, Collier routes still outperform East Liberty routes by 5.4 pp. This could reflect differences in traffic conditions in the western suburbs, garage-level operational practices (scheduling, dispatch, maintenance), or corridor-specific factors not captured by stop count and span alone.

West Mifflin's poor raw performance, by contrast, is largely explained by route structure: it operates the long eastern-corridor routes, and after controlling for that, it is statistically indistinguishable from East Liberty.

The R² increase from 0.31 to 0.41 suggests that garage assignment captures roughly 10% of OTP variance beyond what stop count and span explain – a nontrivial amount that warrants further investigation with operational data (staffing, vehicle age, traffic conditions by corridor).

Caveats

• The current_garage field is a snapshot; historical garage assignments are not available. If routes were reassigned between garages, the analysis would not capture that (though the data shows no garage changes for any route).
• The controlled model uses only stop count and span as structural controls. Adding further controls (e.g., traffic density, road type, schedule slack) could reduce or eliminate the garage effect.
• The F-test assumes normally distributed residuals; the Kruskal-Wallis test (non-parametric) is more robust but does not support covariates.
• South Hills Village (n=3 rail routes) and Incline (excluded, no OTP data) are too small for meaningful comparison and are excluded from the controlled model.

Summary

Weekend ridership has recovered far more strongly than weekday ridership since COVID. As of October 2024, Saturday service is at 90.7% of its January 2019 level while weekday service is at just 64.5%. Weekend's share of total ridership rose from 13.6% pre-COVID to 17.8% post-2023, a +4.2 pp structural shift. The weekend-to-weekday ridership ratio does not significantly correlate with route-level OTP (Pearson r = -0.20, p = 0.097).

Key Numbers

• Weekday recovery (Oct 2024 vs Jan 2019): 64.5% – weekday ridership has not recovered
• Saturday recovery: 90.7% – nearly fully recovered
• Sunday recovery: 83.9%
• Weekend share pre-COVID (Jan 2019 – Feb 2020): 13.6%
• Weekend share post-2023 (Jan 2023 – Oct 2024): 17.8%
• Shift: +4.2 pp toward weekend travel
• 74 routes with 6+ months of all three day types for route-level analysis
• 67 routes with both weekend ratio and OTP data for correlation

Observations

• The indexed ridership chart shows a dramatic divergence after COVID. All three day types crashed in spring 2020, but Saturday and Sunday rebounded much faster and more completely than weekday service.
• The weekend share chart shows a step-change during COVID (weekend share spiked to ~25% when weekday commuting collapsed) followed by a partial return, stabilizing around 17-18% – well above the pre-COVID 13-14% level.
• Route-level weekend ratios vary widely: median 0.97 (roughly equal weekend and weekday ridership per day of service), but ranging from 0.29 (route BLSV, heavily weekday-oriented) to 1.85+ for some routes.
• The correlation between weekend ratio and OTP is weakly negative (r = -0.20) but not statistically significant at alpha = 0.05. Routes with higher weekend share do not have meaningfully different OTP.

Discussion

The 26-percentage-point gap in recovery between weekday (64.5%) and Saturday (90.7%) service is the headline finding. This is consistent with national trends: remote and hybrid work has permanently reduced weekday commuting, while discretionary weekend travel has largely returned. For PRT, this means:

1. Revenue and planning implications: The traditional weekday-peak service model serves a shrinking share of total demand. Weekend service, historically treated as reduced-frequency filler, now carries a proportionally larger role.
2. OTP is not driving the gap: Weekend-heavy routes do not have significantly different OTP, suggesting the weekday ridership collapse is driven by exogenous factors (remote work) rather than service quality differences between day types.
3. Seasonal patterns visible: Both Saturday and Sunday series show strong seasonal swings (summer peaks, winter troughs) that are more pronounced than weekday patterns, consistent with discretionary travel being more weather-sensitive.

Caveats

• The avg_riders field is an average daily ridership for each month, not a total. Multiplying by day_count gives an estimate of total monthly riders, but this assumes uniform ridership across all days of a given type within a month.
• The January 2019 baseline is a single month; seasonal effects mean the indexed values fluctuate even in the pre-COVID period. The recovery percentages should be interpreted as approximate.
• Some routes have extreme weekend ratios (e.g., route 68 at 239x) likely due to very low weekday ridership rather than high weekend ridership. These outliers are excluded from the OTP correlation by the 6-month minimum and OTP data join.
• OTP data is not available by day type – the otp_monthly table contains a single OTP value per route per month, so we cannot directly compare weekday vs weekend OTP.

Summary

Ridership is moderately concentrated on low-OTP routes. The bottom quintile of routes by OTP (Q1, avg 61.2%) carries 29.6% of all ridership (32.7% bus-only), far more than its 20% "fair share." Half of all bus ridership is carried by just 33 of 89 routes, all with OTP below 66.8%. The Gini concentration index is modest (0.068 all routes, 0.145 bus-only), indicating the inequity is real but not extreme.

Key Numbers

• Gini concentration index: 0.068 (all routes), 0.145 (bus-only)
• 50% of ridership carried by 39/93 routes with OTP < 68.0% (all); 33/89 routes with OTP < 66.8% (bus)
• Q1 (worst OTP quintile): 19 routes, avg OTP 61.4%, carries 29.6% of ridership
• Q5 (best OTP quintile): 18 routes, avg OTP 80.9%, carries 23.4% of ridership
• Q4 (second-best): 18 routes, avg OTP 72.5%, carries only 10.2% of ridership
• 93 routes with 12+ months of paired OTP and ridership data

Observations

• The quintile distribution is U-shaped: Q1 (worst) and Q5 (best) carry the most ridership, while Q3-Q4 (middle) carry the least. This reflects two distinct high-ridership populations: heavily-used local bus routes with poor OTP (Q1) and rail/busway routes with good OTP and high ridership (Q5).
• The bus-only analysis sharpens the inequity: removing rail from Q5 drops its ridership share from 23.4% to 17.6%, while Q1 rises from 29.6% to 32.7%. Nearly a third of bus riders are on the worst-performing quintile of routes.
• The Gini index is low (0.068 all, 0.145 bus) because the concentration is moderate, not extreme. Ridership doesn't pile onto a handful of terrible routes – it's spread across many poor-to-mediocre routes, with a few high-performing routes also carrying substantial ridership.
• The Lorenz curve bows above the diagonal throughout, confirming that at every point along the OTP spectrum, cumulative ridership exceeds what equal distribution would predict. The departure is most visible in the first 20-40% of routes (worst OTP).

Discussion

The equity picture is mixed. On one hand, the worst-performing routes carry a disproportionate share of riders – nearly 30% of ridership on the bottom 20% of routes. On the other hand, the best routes (Q5) also carry substantial ridership, so it is not the case that reliable service is reserved for lightly-used routes. The U-shape reflects PRT's system structure: high-ridership corridors tend to be either long, many-stop local bus routes (which have poor OTP due to route complexity, per Analysis 07) or dedicated right-of-way routes (rail/busway, which have good OTP). Middle-performing routes tend to be lower-ridership suburban and express services.

The bus-only Gini (0.145) is more than double the all-mode Gini (0.068), confirming that rail's presence in Q5 masks a more pronounced equity problem within bus service. If PRT seeks to improve the rider-weighted experience, targeting the Q1 bus routes (avg OTP 61.2%, 32.7% of bus ridership) offers the highest human impact per intervention.

Caveats

• The Gini index here measures concentration of ridership across OTP ranks, not income inequality. A positive value means riders disproportionately use low-OTP routes; it does not imply any particular policy threshold.
• Ridership is averaged across all months, which weights the pre-COVID period (higher ridership) more heavily. Post-COVID ridership redistribution may have shifted the concentration pattern.
• OTP is route-level, not trip-level. A rider's actual experience depends on which trips they take, not just their route's monthly average.
• The quintile boundaries are sensitive to the number of routes. With 93 routes, each quintile contains 18-19 routes; small changes in route composition could shift the boundaries.

Summary

Adding log-transformed average weekday ridership to the Analysis 18 multivariate model does not significantly improve explanatory power. The F-test for the ridership term is not significant (F = 2.53, p = 0.116), and R² increases by only 1.5 pp (from 0.499 to 0.514). Ridership is not collinear with stop count or span (VIF = 1.73), but it is largely redundant with the existing predictors – once route structure is controlled for, knowing how many people ride a route tells you almost nothing additional about its OTP.

Key Numbers

• F-test for log_riders (all routes): F = 2.53, p = 0.116
• F-test for log_riders (bus only): F = 2.55, p = 0.114
• log_riders beta weight: -0.16 (weakly negative, not significant)
• VIF for log_riders: 1.73 (no multicollinearity concern)
• Ridership-only model explains just 23.2% of variance (vs 49.9% for structural model)

Expanded model coefficients

Observations

• The base model replicates Analysis 18's results closely (R² = 0.499 here vs 0.472 in Analysis 18; the small difference is because this analysis restricts to routes with ridership data, dropping 0 routes from the 92-route sample).
• Log ridership has a weakly negative coefficient (beta = -0.16): higher-ridership routes tend to have slightly worse OTP after controls, but the effect is not statistically significant. This is consistent with Analysis 19's finding that ridership-weighted OTP is slightly higher than trip-weighted – the two observations are not contradictory because the relationship is weak and confounded.
• Log ridership is surprisingly uncorrelated with stop count (r = +0.15, p = 0.16) and span (r = -0.00, p = 1.00). It is most strongly correlated with weekend_ratio (r = +0.57) – routes with more riders tend to have relatively more weekend service.
• The ridership-only model (log_riders + is_rail, R² = 0.232) explains less than half the variance of the structural model (0.499), confirming that ridership is a weak proxy for the real drivers of OTP (stop count and span).
• All VIFs remain below 3.0 in the expanded model, so multicollinearity is not a concern.

Discussion

This is a clean null result. Ridership does not add meaningful information to the OTP model once route structure is accounted for. The practical implication is that PRT does not need to worry that high ridership per se degrades OTP – the routes with poor OTP happen to have high ridership because they are long, many-stop local bus corridors, not because passenger volumes cause delays. This is consistent with Analysis 10's finding that trip frequency does not predict OTP.

The weak negative direction of the ridership coefficient (-0.16 beta) is suggestive but not significant, and it could reflect residual confounding (high-ridership routes serve congested urban corridors) rather than a causal ridership-to-delay mechanism.

Caveats

• Ridership is measured as average daily weekday riders per route, not per-trip load. Per-trip crowding data would better test the hypothesis that passenger volumes cause delays through dwell time.
• The log transform assumes diminishing marginal effects; a linear specification also fails to reach significance (not shown).
• The sample is restricted to 92 routes with both OTP and ridership data; 6 OTP-only routes are excluded.
• As with Analysis 18, the model's unexplained 50% of variance likely requires operational data (traffic, staffing, schedule slack) not available in this dataset.

Summary

Total traffic volume (AADT) does not explain OTP variance after controlling for structural features (F=0.011, p=0.92). However, truck percentage is a significant predictor (p=0.006), jointly boosting R2 from 0.40 to 0.45. Routes with higher truck traffic perform better on-time, likely because truck-heavy corridors tend to be wider arterials with fewer stops and more predictable traffic flow.

Key Numbers

• 89 routes analyzed (88 bus, 1 rail) after filtering match_rate >= 0.3
• Base model (6 structural features): R2 = 0.40, Adj R2 = 0.36
• Adding log(AADT): R2 = 0.40 (+0.0001), p = 0.92 – not significant
• Adding log(AADT) + truck_pct: R2 = 0.45 (+0.05), joint F = 3.97, p = 0.023
• Truck percentage beta weight: +0.26 (p = 0.006), third-strongest predictor
• VIF for log_aadt = 1.17 – no multicollinearity concern
• AADT range across matched routes: 4,181 – 15,748 vehicles/day
• Top AADT routes: G3 (15,748), 28X (15,328), P12 (15,162)

Observations

• Traffic volume is orthogonal to OTP once structural features are controlled. The bivariate correlation is weak (r = +0.01) and the partial residual plot shows no trend. Routes on high-traffic roads perform similarly to those on quieter ones.
• Truck percentage captures road type, not congestion. The positive coefficient (+0.021 OTP per 1% truck share) suggests that truck-heavy routes operate on highways/arterials with infrastructure advantages (dedicated lanes, longer signal phases, wider roads).
• The three excluded routes (BLUE, P1, SLVR) are rail/busway with match_rate < 0.3, confirming that the PennDOT road network does not cover dedicated transit rights-of-way.
• Bus-only subgroup shows the same null result: log_aadt F = 0.011, p = 0.92.
• The spatial match rate is high (median 80%), indicating good coverage of the PennDOT road network for bus routes.

Discussion

The headline result is a null: traffic volume, the leading candidate for explaining the remaining 50% of OTP variance after structural features, contributes essentially nothing (R2 change of 0.01%). This is not a measurement failure – the VIF of 1.17 confirms that AADT is nearly orthogonal to stop count and span, so it had every opportunity to capture independent variance. It simply doesn't.

Why not? The most likely explanation is that AADT measures the wrong thing. Annual average daily traffic smooths over the peak-hour congestion that actually delays buses. A road carrying 15,000 vehicles/day spread evenly across 24 hours is very different from one carrying the same total with 40% concentrated in two rush-hour peaks. PRT buses operate disproportionately during those peaks, so the congestion they experience is poorly proxied by a 24-hour average. Directional, time-of-day traffic counts – or better yet, speed/travel-time data from probe vehicles – would be a more direct test.

The truck percentage finding is the genuine contribution of this analysis. At +0.26 beta weight (third-strongest after stop count and span), truck share adds 5 percentage points of explained variance. But this almost certainly proxies for road classification rather than a direct truck-bus interaction. Roads with high truck percentages tend to be state highways and major arterials – wider, with longer signal cycles, fewer pedestrian crossings, and more predictable traffic flow. The truck_pct variable is effectively encoding "this route runs on a highway" in a way that is_premium_bus failed to capture (since many non-premium routes also use arterial segments for part of their alignment).

This connects to the broader model-building narrative across Analyses 18, 26, and 27. The base model (stop count + span + mode) explains ~40% of variance. Adding n_munis as a suppressor pushes it to ~47%. Adding truck_pct pushes it to ~45% on the traffic-matched subsample. Ridership (Analysis 26) added nothing. The cumulative picture is that roughly half of OTP variance is explained by route geometry and road type, and the other half likely requires operational data (schedule padding, driver availability, vehicle condition, real-time traffic conditions) that is not in this dataset.

For policy, the null AADT result is actually useful: it suggests that rerouting buses to lower-traffic roads would not improve OTP, since traffic volume per se is not the problem. The truck_pct finding, if it indeed proxies for road type, suggests that routes spending more of their alignment on arterials (vs. neighborhood streets) perform better – consistent with the stop count finding, since arterial segments typically have fewer stops per mile.

Caveats

• AADT is an annual average; it does not capture peak-hour congestion, which is when buses run most frequently and are most affected. Directional or time-of-day traffic data would be a stronger test.
• PennDOT covers state routes; local streets (where many bus routes run) may be underrepresented.
• The truck_pct finding may proxy for road classification rather than a direct causal mechanism.
• The spatial matching uses a 30m buffer, which may associate routes with adjacent parallel roads in dense urban areas.

Summary

Weather variables show moderate raw correlations with system OTP (freeze_days r=+0.44, mean_tmin r=-0.40, snow_days r=+0.40) that strengthen after detrending (freeze_days r=+0.57, mean_tmin r=-0.57), but these correlations are counterintuitive – colder, snowier months have better OTP. Weather jointly adds 15pp of R2 beyond a linear trend (F=3.44, p=0.008) but does not significantly improve on month dummies (F=0.92, p=0.48). The seasonal pattern from Analysis 06 is partially explained by weather – weather adjustment flattens the winter peak by ~2.4pp and lifts the September trough by ~1.3pp – but month dummies add no significant additional explanatory power beyond weather either (F=1.09, p=0.39). At the route-month level with cluster-robust standard errors, no weather variable is significant (all p>0.12), indicating weather effects are too small relative to route-level noise to detect in the panel.

Key Numbers

• Detrended correlations (n=66 months): freeze_days r=+0.57, mean_tmin r=-0.57, mean_wind r=+0.55, snow_days r=+0.46, mean_tmax r=-0.56 (all p<0.001)
• Weather + trend regression (n=72): R2=0.43, vs trend-only R2=0.28, weather adds +15pp (F=3.44, p=0.008)
• Month-only model: R2=0.50; Weather-only model: R2=0.43; Combined: R2=0.54
• F-test (weather added to months): F=0.92, p=0.48 – weather does NOT improve on month dummies
• F-test (months added to weather): F=1.09, p=0.39 – months do NOT improve on weather either
• Route-level panel (n=6,672, 72 clusters): R2=0.045; no variable significant with cluster-robust SEs
• Seasonal adjustment: January raw 70.8% -> adjusted 68.4% (-2.4pp); September raw 64.0% -> adjusted 65.3% (+1.3pp)
• Only 1 of 11 month dummies significant in combined model (September, p=0.039)

Observations

• The raw correlations confirm Analysis 06's finding: winter months have better OTP. This is not despite the weather – it is correlated with cold weather features (freeze days, snow days, low temperatures, high wind).
• After detrending, correlations strengthen substantially (freeze_days: 0.44 -> 0.57), indicating the seasonal weather-OTP relationship is not an artifact of shared secular trends.
• Temperature variables show the strongest detrended correlations (mean_tmin r=-0.57, mean_tmax r=-0.56), meaning warmer months systematically have worse OTP.
• Precipitation (total_precip) has a weak negative correlation (r=-0.23 detrended, p=0.07) – wetter months have slightly worse OTP, but this is the expected direction and not statistically significant.
• In the combined model, weather and month dummies are collinear enough that neither adds significantly to the other. Both capture the same seasonal signal through different variables.
• Weather adjustment partially flattens the seasonal profile: it reduces the January peak by 2.4pp and lifts September by 1.3pp, narrowing the best-to-worst spread from 6.8pp to 3.8pp.
• The panel regression (Block C) shows weather effects are tiny at the route level (R2=4.5%), and cluster-robust SEs (acknowledging that weather is constant within months) eliminate all significance.

Discussion

The key finding is that weather and seasonality are statistically interchangeable at the system level – they capture overlapping variance, and neither adds significantly beyond the other. This means the Analysis 06 seasonal pattern can be described as a weather pattern (cold months = better OTP) but we cannot determine whether weather causes the pattern or merely co-occurs with other seasonal factors (school schedules, construction seasons, ridership patterns).

The counterintuitive direction (cold = better OTP) suggests the mechanism is not weather-as-impediment but rather seasonal demand and operational patterns: winter reduces ridership and road congestion, improving schedule adherence despite worse driving conditions. Snow and cold are proxies for lower demand, not direct causes of better performance.

The panel regression null result is important: even though system-level correlations are strong (r>0.5), weather variation explains only 4.5% of route-month OTP variation, and this disappears with proper clustering. This indicates weather is a system-level seasonal modulator rather than a route-level predictor – all routes respond similarly to weather, so it provides no discriminating power for individual route performance.

Caveats

• n=72 months is small for a 17-parameter model (Block B combined). The F-tests have limited power to distinguish between month dummies and weather variables.
• Weather station ~20km from downtown: Pittsburgh Airport weather may not perfectly represent conditions on specific bus routes, though monthly aggregation minimizes this concern.
• AWND (wind speed) has 5 missing daily values (0.2%), unlikely to affect monthly aggregates.
• Collinearity between weather and month-of-year is inherent – weather is seasonal. The F-tests correctly diagnose this overlap but cannot resolve causality.
• No extreme-event analysis: daily weather extremes (ice storms, heat waves) may have strong route-level effects that are averaged away in monthly aggregation.
• Counterintuitive cold = better OTP may reflect omitted variables (construction, school, ridership) rather than a direct cold-weather benefit.

Summary

Schedule changes (pick period transitions) are associated with a small but statistically significant positive OTP shift on average, though the effect is weak and does not differ significantly by event type (increase, cut, or neutral).

Key Numbers

• 738 schedule change events detected across 101 routes (Nov 2016 – Mar 2021)
• Mean OTP delta: +0.6 pp (t=2.95, p=0.003) – schedule changes are followed by slightly higher OTP on average
• By event type:

- Service increases (+118 trips/day avg): +1.3 pp OTP delta (n=110) - Service cuts (-64 trips/day avg): +0.1 pp OTP delta (n=215) - Neutral (same trips, new schedule): +0.8 pp OTP delta (n=413)

• Kruskal-Wallis across types: H=4.03, p=0.13 – no significant difference between event types
• Trip delta vs OTP delta: Pearson r=0.072 (p=0.050), Spearman rho=0.074 (p=0.045) – marginally significant positive association

Observations

• The dominant event type is "neutral" (413 of 738) – same trip count, different schedule period. This suggests most pick transitions are schedule restructurings rather than service level changes.
• Service increases show the largest OTP improvement (+1.3 pp), while service cuts show nearly no change (+0.1 pp). However, the Kruskal-Wallis test does not detect a significant difference, so this pattern may be noise.
• COVID period events (n=184) show a smaller mean delta (+0.2 pp) than non-COVID events (+0.8 pp), possibly because the COVID period involves confounding system-wide disruptions.
• The correlation between trip count change and OTP change is marginally significant (p~0.05) but very weak (r=0.07), explaining less than 1% of variance.

Discussion

The statistically significant but tiny positive mean delta (+0.6 pp) is best interpreted as evidence that schedule changes are not harmful to OTP, rather than evidence that they improve it. The effect size is operationally negligible – less than 1 percentage point – and the lack of differentiation across event types (Kruskal-Wallis p=0.13) means we cannot conclude that service increases help or that service cuts hurt.

The most striking finding is the dominance of "neutral" events (413 of 738). Most pick period transitions leave trip counts unchanged, meaning PRT's schedule restructurings are primarily about rearranging timing, not adding or removing service. These neutral events still show a +0.8 pp OTP delta, which is consistent with the hypothesis that PRT uses schedule changes as opportunities to adjust running times or pad recovery time – operational improvements that would improve OTP without changing trip frequency.

The marginal Spearman correlation (rho=0.074, p=0.045) aligns with the direction suggested by Analysis 30's pre-COVID subperiod (adding trips slightly degrades OTP), but in the opposite direction here – adding trips is associated with better OTP. This apparent contradiction dissolves when considering that Analysis 29 measures 3-month average shifts around discrete events, while Analysis 30 measures month-over-month continuous variation. The schedule change event likely captures a package of operational adjustments (new running times, rerouted deadheads, adjusted layover) that happen to coincide with trip count changes, not a pure frequency effect.

For policy, the null Kruskal-Wallis result is the most actionable finding: it suggests PRT can adjust service levels (up or down) without expecting systematic OTP consequences. OTP is determined by factors other than how many trips are scheduled.

Caveats

• The 3-month averaging window means overlapping events can contaminate each other. Routes with frequent schedule changes (every 2-3 months) have correlated before/after windows.
• The positive mean OTP delta could reflect a selection effect: PRT may time schedule changes to coincide with seasonal improvements or known operational gains.
• Causality cannot be established – schedule changes and OTP improvements may share common causes (e.g., new management priorities).

Summary

Within-route month-over-month changes in scheduled trip frequency have no significant relationship with OTP changes after detrending. This null result holds across all routes, bus-only, and in both pre- and post-COVID subperiods.

Key Numbers

• 2,374 delta observations from 93 routes over 27 months (Jan 2019 – Mar 2021)
• All routes: slope=0.00002, Pearson r=0.018 (p=0.39), Spearman rho=-0.030 (p=0.15)
• Bus only (n=2,288): slope=0.00002, Pearson r=0.023 (p=0.26), Spearman rho=-0.031 (p=0.13)
• Pre-COVID (n=1,195): slope=-0.004, r=-0.052 (p=0.07) – marginally negative
• Post-COVID (n=1,179): slope=0.00002, r=0.030 (p=0.31) – null

Observations

• The overall effect is essentially zero: a change in daily trip count explains less than 0.1% of the variance in detrended OTP changes.
• This confirms Analysis 10's cross-sectional null finding with a stronger longitudinal design that controls for all time-invariant route characteristics (geography, length, mode).
• The pre-COVID period shows a marginally significant negative slope (r=-0.052, p=0.07), suggesting that adding trips slightly degraded OTP when the system was running near capacity. However, this is borderline and does not survive Bonferroni correction for multiple comparisons.
• The post-COVID period shows no relationship at all, consistent with reduced ridership creating slack in the system.
• The Spearman correlations are consistently negative but not significant, hinting that the relationship (if any) is slightly negative – more service slightly worsens on-time performance – but the effect is too small to detect reliably in this sample.

Discussion

This null result is the most methodologically rigorous frequency-OTP test in the project. Analysis 10 was cross-sectional (comparing different routes at one point in time) and confounded by route characteristics – long routes have both more trips and worse OTP for structural reasons. This analysis controls for all time-invariant route features by using within-route changes over time, and detrends to remove system-wide shocks. The result is unambiguous: trip frequency changes do not predict OTP changes within routes.

The marginally negative pre-COVID slope (r=-0.052, p=0.07) is the one signal worth noting. Before COVID, the system was operating near capacity, and adding trips to an already-constrained route may have slightly degraded schedule adherence – each additional trip competes for the same road space, layover time, and driver availability. After COVID reduced demand, this constraint relaxed and the effect disappeared. This is consistent with a capacity-constrained model where frequency only matters at the margin when the system is near saturation, and is irrelevant otherwise.

The policy implication reinforces what emerged across Analyses 10, 26, and 29: scheduled service frequency is not a lever for OTP improvement. Routes don't get more on-time by running fewer trips, and they don't get less on-time by running more. The ~50% of OTP variance explained by the multivariate model (Analysis 18) comes from structural features (stop count, route length, mode), and the remaining ~50% likely reflects operational factors (schedule padding, driver availability, real-time traffic variability) that are orthogonal to how many trips are scheduled.

The 27-month window is a genuine limitation. A longer panel with more schedule variation – particularly one that captures the post-2021 period when PRT may have restructured service – could provide more statistical power. Extending the WPRDC data or obtaining historical GTFS archives would strengthen this null finding or reveal effects that 27 months cannot detect.

Caveats

• The panel covers only 27 months, limiting statistical power for detecting small effects.
• Month-over-month trip changes are often zero (same pick period), reducing the effective variation in the independent variable.
• OTP is measured monthly while schedule changes can occur mid-month, introducing measurement noise.
• System-wide detrending removes the COVID shock but may also remove genuine correlated service changes (e.g., if all routes cut service and all improved OTP simultaneously).

Summary

43% of all stop-route combinations in the PRT system see fewer than 5 daily boardings+alightings on weekdays, and nearly all of these have a same-route neighbor within 400 m walking distance. Removing these low-usage stops could yield an average OTP improvement of +3.2 percentage points per route, with the highest-impact routes gaining up to +10 pp. The top candidates are long suburban/flyer routes with many lightly used stops along corridors.

Key Numbers

• 11,461 stop-route combinations in the pre-pandemic weekday data
• 4,991 (43%) are low-usage (< 5 avg daily ons+offs)
• 4,963 of those have a neighbor on the same route within 400 m (consolidation candidates)
• 87 of 90 routes (97%) matched to OTP data have at least one candidate
• Median candidates per route: 44 stops
• Regression slope: each stop removed is associated with +0.059 pp OTP
• Average estimated OTP gain: +3.2 pp across routes with candidates
• Maximum estimated OTP gain: +10.2 pp (Route 59, Mon Valley – 174 candidate stops)

Observations

• Flyer/express routes have the most candidates: P10 (167), P16 (159), O5 (148) – these long-distance routes serve many stops with minimal usage along the way.
• Route 59 (Mon Valley) tops the list with 174 candidates out of 334 stop-route pairs, representing a potential 52% reduction in stops.
• The candidate map shows candidates distributed system-wide, with particularly dense clusters in outer suburban corridors where stop spacing is tight but usage is low.
• Almost all low-usage stops (99.4%) have a nearby neighbor, meaning very few riders would lack a within-walking-distance alternative.
• The OTP gain estimate is conservative: the regression slope (-0.059 pp/stop) comes from cross-sectional variation, not from an experiment. Actual gains from targeted consolidation could differ.

Discussion

What the data shows

Analysis 07 established that stop count is the strongest single predictor of poor OTP (r = -0.53), and this analysis shows that nearly half the system's stop-route pairs see trivially low usage. The correlation between stop count and OTP is real and robust across multiple specifications.

The concentration of candidates on flyer routes (P10, P16, O5) is intuitive: these routes traverse long suburban corridors where stops were placed at frequent intervals to maximize coverage, but actual demand clusters at a few park-and-ride or transfer locations.

Why the OTP gain estimate is likely overstated

The +3.2 pp average gain estimate assumes each stop removed saves equivalent time, but PRT bus drivers already skip stops where no one is waiting and no one has signaled to alight. A low-usage stop with <5 daily boardings is empty on the vast majority of individual bus trips, meaning the bus already passes it without stopping most of the time. Removing the sign does not change this operational reality.

The cross-sectional regression slope (-0.059 pp/stop) captures the fact that routes with many stops are structurally different – they are longer, serve denser urban corridors with more traffic signals, and have higher cumulative probability of someone being at the next stop. These are route design characteristics, not marginal effects of individual stops. The causal effect of removing a single low-usage stop is likely well below the regression estimate.

Analysis 34 (Ridership Concentration) reinforces this interpretation: per-stop ridership concentration has no correlation with OTP (r = -0.016, p = 0.88), suggesting dwell time from passenger volumes is not the dominant mechanism. The stop count/OTP relationship is better understood as a proxy for route design philosophy (local vs limited-stop vs express) rather than a per-stop causal lever.

Accessibility and equity concerns

The 400 m walk-distance filter assumes riders can walk to the next stop, but this may not hold for riders with disabilities, elderly riders, or those with mobility limitations – particularly given Pittsburgh's hilly terrain. ADA compliance is not just a legal requirement but a core service obligation. Any consolidation program would require stop-by-stop accessibility review. Some low-usage stops may also serve riders making short trips where incremental stop spacing is the primary value of the bus service.

Reframing the finding

The stop count/OTP relationship is best read as evidence that route design with fewer, better-spaced stops outperforms local-stop design – which is already reflected in the busway/express vs local gap (Analysis 02). The policy implication points more toward limited-stop or express overlays on high-ridership corridors than toward individual stop removal. Converting low-usage suburban segments to limited-stop service (as the flyer route candidates suggest) is more defensible than piecemeal stop removal, because it redesigns the service pattern rather than degrading existing local coverage.

Stop consolidation remains politically sensitive. Community opposition to stop removal often exceeds what ridership data would justify. A phased approach – starting with stops below 1 rider/day that have a neighbor within 200 m, with accessibility review – would minimize controversy while testing whether actual OTP gains materialize.

Caveats

• The OTP gain estimate is likely overstated because buses already skip empty stops operationally; removing the sign at a stop that is already being passed most trips has minimal time savings.
• The regression slope is a cross-sectional system-wide average reflecting route design differences, not a causal per-stop marginal effect. Individual stop removal may have near-zero impact.
• Accessibility: the 400 m walk-distance filter may be inadequate for riders with disabilities or limited mobility, especially on Pittsburgh's hilly terrain. ADA review is required before any consolidation.
• Short trips: some low-usage stops serve riders making short trips where incremental stop spacing is the primary value of the service.
• Stop usage data is from FY2019 (pre-pandemic); current usage patterns may have shifted.
• Some stops may appear low-usage on one route but serve high volumes on other routes at the same physical location; the data is per stop-route, not per physical stop.
• Projected stop counts can go negative for routes where the CSV has more stop-route combinations than the DB stop count (due to different data vintages).

Summary

Only 7.3% of PRT bus stops have shelters, yet those sheltered stops serve 31% of total system ridership. Sheltered stops have 5x the median daily usage of unsheltered stops (34 vs 7 riders/day). The most striking gap is among regular bus stops, where just 7% have shelters despite serving the vast majority of riders. Several of the system's busiest stops – including downtown intersections with 2,000+ daily boardings – lack any shelter.

Key Numbers

• 6,719 unique physical stops in the pre-pandemic weekday data
• 491 (7.3%) have shelters; 6,228 do not
• Sheltered stops: median 34.3/day, mean 162.6/day
• Unsheltered stops: median 6.5/day, mean 28.9/day
• Sheltered stops serve 30.7% of total system ridership despite being only 7% of stops
• Mann-Whitney U test: p = 9.2e-84 (sheltered stops have significantly higher usage)
• Bus mode: only 7% sheltered; Busway: 73%; Light Rail: 100%

Observations

• Shelter placement correlates with usage but leaves major gaps. The top 20 unsheltered stops each see 1,200-2,800 daily riders. The busiest unsheltered stop (7th St at Penn Ave, 2,841/day) handles more riders than all but a handful of sheltered stops.
• Downtown Pittsburgh has the biggest equity gap. Almost all top unsheltered stops are in the downtown/Oakland corridor (5th Ave, Liberty Ave, Wood St, Stanwix St). These are high-exposure locations where riders wait in weather.
• PAAC and City of Pittsburgh own most shelters (197 and 174 respectively), with City shelters at higher-usage stops on average (204 vs 165/day).
• Lamar (advertising) shelters skew low-usage: 100 shelters averaging only 26 riders/day, suggesting ad-driven placement rather than ridership-driven.
• Heffner shelters also serve low-usage stops (avg 3/day), further suggesting non-ridership factors drive some shelter placement.
• "Envision Downtown" and "Other" shelters serve the absolute highest-volume locations (2,913 and 1,090/day respectively), but account for only 5 stops total.

Discussion

The shelter coverage gap represents a tangible rider experience problem. The 20 busiest unsheltered stops collectively serve ~35,000 riders per day who wait without weather protection. Given Pittsburgh's climate (Analysis 28 showed snow days and freeze days significantly affect OTP), shelter absence at high-volume stops compounds the negative experience of unreliable service.

The divergence between shelter owners reveals different placement strategies. PAAC and City of Pittsburgh place shelters at moderately high-usage stops (165-204/day), following a ridership-informed approach. Lamar's advertising-driven placements (26/day average) prioritize visibility for ad revenue over rider need, and Heffner's placements (3/day) appear driven by factors entirely unrelated to ridership. This suggests the advertising-shelter model, while providing free infrastructure, does not align with transit equity goals.

The Pareto finding from Analysis 34 (2% of stops serve 50% of riders) frames the opportunity: sheltering just the top 150 unsheltered stops would reach a large share of unprotected riders. At typical shelter costs of $15-30K per installation, covering the top 20 unsheltered stops would cost $300-600K while protecting ~35,000 daily riders – a strong return on investment.

The downtown equity gap is particularly striking because these stops are the most visible face of the transit system. Visitors and new riders encountering a 2,800-rider/day stop with no shelter receive a signal about the system's investment priorities. Addressing the downtown/Oakland gaps would improve both rider experience and public perception.

Caveats

• The shelter field in the WPRDC data may not be fully up to date; some shelters may have been added or removed since the data was compiled.
• "No Shelter" is the default – stops with missing shelter data are treated as unsheltered, which may slightly overcount the unsheltered total.
• Usage data is pre-pandemic (FY2019); current ridership patterns at specific stops may have shifted.
• Light rail shows 100% coverage but only 1 stop appears in the data, so the mode comparison is limited for rail.

Summary

System-wide weekday ridership fell 63% between the pre-pandemic baseline (Sep 2019/Jan 2020) and the pandemic period (Sep 2020/Apr 2021). The loss was remarkably uniform geographically: the median stop lost ~60% regardless of whether it was in downtown, the inner ring, or the outer suburbs. The largest absolute losses were concentrated at high-volume downtown and university-area stops, while outer suburban stops showed slightly better retention in aggregate.

Key Numbers

• 6,719 stops with matched pre/post data; 6,556 with pre-pandemic usage > 0
• System total weekday usage: 259,783 -> 95,798 (-63.1%)
• Median stop-level change: -60.2%; Mean: -50.7%
• Downtown (< 2 km): median -60%, aggregate -64.1% (n=369)
• Inner ring (2-8 km): median -62%, aggregate -65.7% (n=2,658)
• Outer ring (> 8 km): median -59%, aggregate -55.7% (n=3,529)
• By mode: Bus -60%, Busway -58%, Light Rail -56%
• Largest single-stop loss: Liberty Ave at Market St (-2,329 riders/day, -73%)

Observations

• The pandemic hit uniformly across geography. All three zones saw median declines of 59-62%. The hypothesis that downtown would lose disproportionately more (due to remote work) is only weakly supported: downtown's aggregate loss (-64%) is slightly above average but well within the range of the inner ring (-66%).
• The inner ring actually lost the most in aggregate (-65.7%), likely because it contains high-volume university (Oakland) and hospital-adjacent stops that saw steep declines.
• Outer suburbs retained ridership slightly better (-55.7% aggregate), consistent with more essential/transit-dependent riders in these areas.
• The biggest absolute losses are clustered in two corridors: downtown (Liberty Ave, Smithfield St) and Oakland/university area (5th Ave at Thackeray, Forbes Ave at Morewood). These are commuter and student-heavy stops.
• The distribution is unimodal with a long right tail: most stops lost 40-80%, but a small number gained riders, likely reflecting route restructuring or localized demand shifts.
• Mode differences are minimal: busway and light rail fared marginally better than bus, but only by 2-4 percentage points.

Discussion

The geographic uniformity of ridership loss challenges the narrative that the pandemic disproportionately affected downtown transit. While downtown and Oakland stops did lose the most riders in absolute terms (because they started highest), the rate of loss was nearly identical everywhere. This suggests the pandemic's impact was driven more by system-wide behavioral shifts (remote work, fear of shared spaces) than by location-specific factors.

The slightly better retention in outer suburbs aligns with the "essential worker" hypothesis: riders who depend on transit for non-office jobs continued riding at higher rates. This has implications for service planning – if remote work persists, the ridership center of gravity may permanently shift outward, favoring suburban route investment.

The Oakland/university corridor stands out as a potential recovery target: these stops lost 70-87% of riders, largely due to remote instruction. As universities have returned to in-person operations, these stops may have recovered more than this pandemic-era snapshot shows.

Caveats

• The pandemic period averages Sep 2020 and Apr 2021, which represent different stages of the pandemic; conditions changed rapidly.
• The data captures only weekday usage. Weekend patterns may show different geographic signatures.
• Some stops may have been temporarily closed or rerouted during the pandemic, inflating apparent losses.
• The zone classification uses simple distance rings; a neighborhood-level analysis might reveal more nuance.

Summary

PRT ridership is extremely concentrated: just 2% of stops serve 50% of all weekday riders, and 14% of stops serve 80%. The system-wide Gini coefficient is 0.82, indicating very high inequality in stop-level usage. However, per-route ridership concentration (Gini) has essentially zero correlation with that route's OTP (r = -0.016, p = 0.88), meaning whether a route's riders are clustered at a few stops or spread evenly has no bearing on schedule reliability.

Key Numbers

• 2.2% of stops serve 50% of ridership
• 13.9% of stops serve 80% of ridership
• 27.9% of stops serve 90% of ridership
• System-wide Gini = 0.824
• Per-route Gini range: 0.338 - 0.890 (median 0.649)
• 95 routes with >= 3 stops analyzed
• 90 routes matched to OTP data
• Gini vs OTP (bus-only): Pearson r = -0.016 (p = 0.879), Spearman rho = 0.103 (p = 0.339)

Observations

• The Pareto curve is steep: the top ~150 stops (out of 6,700+) account for half of all weekday boardings and alightings. This is more extreme than a classic 80/20 rule – it's closer to a 2/50 pattern.
• Most stops see very little usage: the median stop handles only ~7 riders/day, while the top stops see 2,000-5,800/day. The bottom 70% of stops collectively serve only 10% of ridership.
• Route-level concentration varies widely: some routes have Gini as low as 0.34 (relatively even usage across stops) while others reach 0.89 (nearly all ridership at a few stops). Flyer/express routes tend to have higher Gini since ridership clusters at downtown endpoints.
• Concentration does not predict OTP. The scatter plot shows no trend at all – the regression line is essentially flat. Routes with highly concentrated ridership perform no better or worse than those with evenly distributed usage.

Discussion

The extreme system-wide concentration (Gini = 0.82) reinforces the stop consolidation finding from Analysis 31: most stops contribute very little ridership, and removing the lowest-usage ones would affect few riders while potentially improving OTP by reducing stop count.

The null result for Gini vs OTP is notable. One might hypothesize that routes with concentrated ridership would have better OTP (less dwell time at most stops), but this doesn't hold. This suggests that dwell time at individual stops is not a dominant factor in OTP variance – the time cost of stopping (deceleration, door opening, acceleration) matters more than the time cost of boarding passengers. This aligns with the Analysis 07 finding that raw stop count, not passenger volume, drives OTP.

The 2/50 concentration ratio has resource allocation implications: if PRT focused infrastructure investment (shelters, real-time signs, ADA upgrades) on just 150 stops, it would reach half of all riders. The current shelter coverage of 7% (Analysis 32) suggests significant room to target the highest-impact locations.

Caveats

• Stop-level usage data is from FY2019; current patterns may differ, especially post-pandemic.
• Gini is computed from stop-route combinations, not physical stops. Routes sharing physical stops may inflate the apparent concentration.
• The OTP data covers a longer time range (2019-2025) than the usage snapshot (2019), so the correlation compares static usage structure against time-averaged OTP.
• Very short routes (< 3 stops) are excluded from the Gini analysis, which drops a few incline and shuttle routes.

Summary

PRT's system-wide boarding/alighting balance is nearly perfect (ratio 1.003), but individual stops show strong directional asymmetry. The top generators (net boardings) are outbound departure points on Smithfield St, 5th Ave, and Liberty Ave in downtown. The top attractors (net alightings) are inbound arrival points on Wood St, Liberty Ave at Gateway, and North Side Station. The directional data confirms a classic radial commuter pattern: inbound trips net +22,385 boardings vs outbound trips net -24,197 (i.e., people board going in and alight going out).

Key Numbers

• 130,121 avg weekday boardings vs 129,684 avg alightings (ratio 1.003)
• 3,103 (46%) stops are net generators; 3,442 (51%) are net attractors; 174 (3%) balanced
• Inbound on/off ratio: 1.36 (net +22,385 boardings)
• Outbound on/off ratio: 0.73 (net -24,197 boardings)
• Top generator: Smithfield St at Sixth Ave (+1,993 net/day)
• Top attractor: Wood St btw Forbes & Fifth (-1,350 net/day)
• Median stop on/off ratio: 0.76 (slight attractor skew)
• 38.8% of stops are strong generators (ratio > 1.5); 48.0% are strong attractors (ratio < 0.67)

Observations

• The network is classically radial. Inbound stops generate a strong net surplus of boardings (+22K/day), meaning suburban riders board inbound and alight downtown. Outbound stops show the mirror: net -24K, as downtown riders board outbound and alight in suburbs.
• Downtown has both strong generators and attractors, on different streets. Smithfield St and 5th Ave are net generators (people boarding outbound departures), while Wood St and Liberty Ave/Gateway are net attractors (people arriving inbound). This reflects the one-way street grid routing buses through different downtown streets for inbound vs outbound.
• Busway stations appear on both lists. Wilkinsburg Station shows split behavior: Platform C is a generator (+837/day, outbound departures from the East Busway) while Platform A is an attractor (-935/day, inbound arrivals). This confirms the station's role as a major suburban interchange.
• North Side Station is the #5 attractor (-994 net/day), consistent with its role as a major inbound terminus where light rail and busway passengers alight.
• Oakland/university stops are generators: 5th Ave opp Thackeray (+871) and Forbes at Morewood (+868) show students boarding outbound to return home.
• The median stop is a slight attractor (ratio 0.76), reflecting that many suburban stops have more people getting off (returning home) than getting on.

Discussion

The boarding/alighting flow pattern is a direct fingerprint of Pittsburgh's commuter geography. The strong inbound-boarding / outbound-alighting asymmetry (+22K/-24K) confirms that PRT operates as a radial commuter network focused on downtown. The slight imbalance (outbound net is 1,800 higher than inbound net) likely reflects "Both"-direction stops that aggregate mixed flows.

The street-level generator/attractor split in downtown is operationally informative: Smithfield St outbound stops need boarding capacity (shelters, queuing space, real-time info), while Wood St inbound stops need alighting capacity (wide sidewalks, clear exits). This differs from a simple "downtown = destination" model and has implications for stop amenity design.

The presence of Oakland as a net generator is notable – it suggests the 5th Ave/Forbes corridor serves as a secondary hub where students and workers board to travel outbound, not just as a destination from downtown. This bidirectional flow may explain why 5th Ave routes face OTP challenges: high dwell time at stops that serve both directions heavily.

For service planning, the net flow data identifies where passenger demand is structurally asymmetric. Routes serving strong generators could potentially benefit from express or limited-stop variants in the outbound direction, while routes terminating at strong attractors could justify higher inbound frequency.

Caveats

• The "direction" field (Inbound/Outbound/Both) groups stops, not individual trips. Stops coded "Both" handle mixed flows that don't cleanly separate.
• Net flow reflects the first stop a person is counted at, not their complete trip. Transfer passengers are counted at each stop they use.
• Pre-pandemic weekday data (FY2019); commuter patterns may have shifted with remote work.
• Physical stops serving multiple routes aggregate flows across routes, which may mask route-specific patterns.